Question 1

Determine whether the function has an inverse function.If it does,find the inverse function. f(x)= x2 + 5

Accepted Answer

A)  $$f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 5$ 
E) No inverse function exists. 
A)  $$f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 5$ 
E) No inverse function exists.

Question 2

Determine whether the function is one-to- one. ​
Y = 3x
​

Accepted Answer

A) No,it isn't one-to-one. 
B) Yes,it is one-to-one. 
A) No,it isn't one-to-one. 
B) Yes,it is one-to-one.

Question 3

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ​
F(x)= |x - 9| + 1
​

Accepted Answer

A) f-1(x)= x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
B) f-1(x)= x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
C) f-1(x)= -x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ -9. 
D) f-1(x)= x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ -9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
E) f-1(x)= -x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ 9. 
A) f-1(x)= x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
B) f-1(x)= x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
C) f-1(x)= -x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ -9. 
D) f-1(x)= x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ -9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
E) f-1(x)= -x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ 9.

Question 4

Use the functions given by $f ( x ) = \frac { 1 } { 125 } x - 1$ and g(x)= x3 to find (f º g)-1. ?

Accepted Answer

A)  $5 \sqrt [ 3 ] { x - 1 }$ 
B)  $125 \sqrt [ 3 ] { x - 1 }$ 
C)  $5 \sqrt [ 3 ] { x + 1 }$ 
D)  $125 \sqrt [ 3 ] { x + 1 }$ 
E)  $5 \sqrt { x + 1 }$ 
A)  $5 \sqrt [ 3 ] { x - 1 }$ 
B)  $125 \sqrt [ 3 ] { x - 1 }$ 
C)  $5 \sqrt [ 3 ] { x + 1 }$ 
D)  $125 \sqrt [ 3 ] { x + 1 }$ 
E)  $5 \sqrt { x + 1 }$

Question 5

Your wage is $11.00 per hour plus $0.50 for each unit produced per hour.So,your hourly wage in terms of the number of units produced x is y = 11 + 0.50x.Find the inverse function.What does each variable represent in the inverse function? ?

Accepted Answer

A)  $y = \frac { x - 11 } { 0.50 }$ x = hourly wage;y = numbers of units produced 
B) y = 11 + 0.50x x = hourly wage;y = numbers of units produced
? 
C)  $$y = \frac { x + 11 } { 0.50 }$$ x = hourly wage;y = numbers of units produced
? 
D)  $y = \frac { 11 - x } { 0.50 }$ x = hourly wage;y = numbers of units produced
? 
E) y = 11 - 0.50x x = hourly wage;y = numbers of units produced
? 
A)  $y = \frac { x - 11 } { 0.50 }$ x = hourly wage;y = numbers of units produced 
B) y = 11 + 0.50x x = hourly wage;y = numbers of units produced
? 
C)  $$y = \frac { x + 11 } { 0.50 }$$ x = hourly wage;y = numbers of units produced
? 
D)  $y = \frac { 11 - x } { 0.50 }$ x = hourly wage;y = numbers of units produced
? 
E) y = 11 - 0.50x x = hourly wage;y = numbers of units produced
?

Question 6

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.? $$g ( x ) = \frac { 4 - x } { 5 }$$ ? ?

Accepted Answer

A)    The function has an inverse. 
B) ?   The function has an inverse. 
C) ?   The function has an inverse. 
D) ?   The function has an inverse. 
E) ?   The function has an inverse. 
A)    The function has an inverse. 
B) ?   The function has an inverse. 
C) ?   The function has an inverse. 
D) ?   The function has an inverse. 
E) ?   The function has an inverse.

Question 7

Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x)= x3 to find g-1 º f-1. ?

Accepted Answer

A)  $4 \sqrt [ 3 ] { ( 4 - x ) }$ 
B)  $- 4 \sqrt [ 3 ] { ( x + 4 ) }$ 
C)  $- 4 \sqrt [ 3 ] { ( x - 4 ) }$ 
D)  $4 \sqrt [ 3 ] { ( x - 4 ) }$ 
E)  $4 \sqrt [ 3 ] { ( x + 4 ) }$ 
A)  $4 \sqrt [ 3 ] { ( 4 - x ) }$ 
B)  $- 4 \sqrt [ 3 ] { ( x + 4 ) }$ 
C)  $- 4 \sqrt [ 3 ] { ( x - 4 ) }$ 
D)  $4 \sqrt [ 3 ] { ( x - 4 ) }$ 
E)  $4 \sqrt [ 3 ] { ( x + 4 ) }$

Question 8

?Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f-1. ??   ?

Accepted Answer

A)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 8 \
\hline
\end{array}
\end{array}$$ 
B)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \
\hline
\end{array}
\end{array}$$ 
C)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$$ 
D)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \
\hline
\end{array}
\end{array}$$ 
E)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$$ 
A)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 8 \
\hline
\end{array}
\end{array}$$ 
B)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \
\hline
\end{array}
\end{array}$$ 
C)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$$ 
D)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \
\hline
\end{array}
\end{array}$$ 
E)  $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$$

Question 9

Restrict the domain of f(x)= x2 + 5 to x ≥ 0.Use a graphing utility to graph the function. ​

Accepted Answer

A) ​   
B)    
C) ​   
D) ​   
E)    
A) ​   
B)    
C) ​   
D) ​   
E)

Question 10

Find the inverse of the one-to-one function.
​
y = 5x + 4
​
f -1(x)= __________

Accepted Answer

Question 11

Use the functions given by f(x)= x + 6 and g(x)= 7x - 3 to find g-1 º f-1. ?

Accepted Answer

A)  $\frac { - x - 3 } { 7 }$ 
B)  $\frac { x + 3 } { 7 }$ 
C)  $\frac { x - 3 } { 7 }$ 
D)  $\frac { x - 3 } { - 7 }$ 
E)  $\frac { x - 7 } { 3 }$ 
A)  $\frac { - x - 3 } { 7 }$ 
B)  $\frac { x + 3 } { 7 }$ 
C)  $\frac { x - 3 } { 7 }$ 
D)  $\frac { x - 3 } { - 7 }$ 
E)  $\frac { x - 7 } { 3 }$

Question 12

Find the inverse of the one-to-one function.​ $y = \frac { 1 } { 8 x }$ ​
f -1(x)= __________

Accepted Answer

Question 13

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​
G(x)= |x + 5| - |x - 5|
​

Accepted Answer

A) ​   The function does not have inverse. 
B) ​   The function does not have inverse. 
C) ​   The function does not have inverse. 
D) ​   The function does not have inverse. 
E)    The function does not have inverse. 
A) ​   The function does not have inverse. 
B) ​   The function does not have inverse. 
C) ​   The function does not have inverse. 
D) ​   The function does not have inverse. 
E)    The function does not have inverse.

Question 14

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ?
F(x)= (x - 5)2
?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 5.The domain of f-1 and the range of f are all real numbers x such that x ? 0. 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 0.The domain of f-1 and the range of f are all real numbers x such that x ? -5. 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 5.The domain of f-1 and the range of f are all real numbers x such that x ? 0. 
D)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 0.The domain of f-1 and the range of f are all real numbers x such that x ? 5. 
E)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? -5.The domain of f-1 and the range of f are all real numbers x such that x ? 0. 
A)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 5.The domain of f-1 and the range of f are all real numbers x such that x ? 0. 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 0.The domain of f-1 and the range of f are all real numbers x such that x ? -5. 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 5.The domain of f-1 and the range of f are all real numbers x such that x ? 0. 
D)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? 0.The domain of f-1 and the range of f are all real numbers x such that x ? 5. 
E)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ ?
The domain of f and the range of f-1 are all real numbers x such that x ? -5.The domain of f-1 and the range of f are all real numbers x such that x ? 0.

Question 15

Find the inverse function of g(x)= x2 - 3 informally. ?

Accepted Answer

A)  $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x - 3 }$ 
B)  $g ^ { - 1 } ( x ) = ( x + 3 ) ^ { 2 }$ 
C)  $$g ^ { - 1 } ( x ) = x ^ { 2 } + 3$$ 
D)  $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x + 3 }$ 
E)  $$g ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$$ 
A)  $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x - 3 }$ 
B)  $g ^ { - 1 } ( x ) = ( x + 3 ) ^ { 2 }$ 
C)  $$g ^ { - 1 } ( x ) = x ^ { 2 } + 3$$ 
D)  $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x + 3 }$ 
E)  $$g ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$$

Question 16

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }$$ ?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Determine whether the function has an inverse function.If it does,find the inverse function. ?
F(x)= -2
?

Accepted Answer

A) f-1(x)= 2 
B)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 }$ 
D) f-1(x)= -2 
E) No inverse 
A) f-1(x)= 2 
B)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 }$ 
D) f-1(x)= -2 
E) No inverse

Question 18

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ​
F(x)= |x + 5|
​

Accepted Answer

A) f​-1(x)= x - 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ -5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
B) f​-1(x)= x + 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ -5. 
C) f​-1(x)= x - 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ 5. 
D) f​-1(x)= x + 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
E) f​-1(x)= x - 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
A) f​-1(x)= x - 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ -5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
B) f​-1(x)= x + 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ -5. 
C) f​-1(x)= x - 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ 5. 
D) f​-1(x)= x + 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
E) f​-1(x)= x - 5 ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0.

Question 19

Find the inverse function of f informally. ?
F(x)= x4
?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = 4 \sqrt { x }$ ? 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt [ 4 ] { x } }$ 
D)  $f ^ { - 1 } ( x ) = ( \sqrt [ 4 ] { x } ) ^ { 4 }$ 
E)  $f ^ { - 1 } ( x ) = - \sqrt [ 4 ] { x }$ 
A)  $f ^ { - 1 } ( x ) = 4 \sqrt { x }$ ? 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt [ 4 ] { x } }$ 
D)  $f ^ { - 1 } ( x ) = ( \sqrt [ 4 ] { x } ) ^ { 4 }$ 
E)  $f ^ { - 1 } ( x ) = - \sqrt [ 4 ] { x }$

Exam 9: Inverse Functions

Determine whether the function has an inverse function.If it does,find the inverse function. f(x)= x2 + 5

Determine whether the function is one-to- one. ​ Y = 3x ​

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ​ F(x)= |x - 9| + 1 ​

Use the functions given by f(x)=1125x−1f ( x ) = \frac { 1 } { 125 } x - 1f(x)=1251​x−1 and g(x)= x3 to find (f º g)-1. ?

Your wage is $11.00 per hour plus $0.50 for each unit produced per hour.So,your hourly wage in terms of the number of units produced x is y = 11 + 0.50x.Find the inverse function.What does each variable represent in the inverse function? ?

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.? g(x)=4−x5g ( x ) = \frac { 4 - x } { 5 }g(x)=54−x​ ? ?

Use the functions given by f(x)=164x−4f ( x ) = \frac { 1 } { 64 } x - 4f(x)=641​x−4 and g(x)= x3 to find g-1 º f-1. ?

?Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f-1. ?? ?

Restrict the domain of f(x)= x2 + 5 to x ≥ 0.Use a graphing utility to graph the function. ​

Find the inverse of the one-to-one function. ​ y = 5x + 4 ​ f -1(x)= __________

Use the functions given by f(x)= x + 6 and g(x)= 7x - 3 to find g-1 º f-1. ?

Find the inverse of the one-to-one function.​ y=18xy = \frac { 1 } { 8 x }y=8x1​ ​ f -1(x)= __________

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​ G(x)= |x + 5| - |x - 5| ​

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ? F(x)= (x - 5)2 ?

Find the inverse function of g(x)= x2 - 3 informally. ?

Select the correct graph,showing f and g are inverse functions.? f(x)=x37,g(x)=7x3f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }f(x)=7x3​,g(x)=37x​ ?

Determine whether the function has an inverse function.If it does,find the inverse function. ? F(x)= -2 ?

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ​ F(x)= |x + 5| ​

Find the inverse function of f informally. ? F(x)= x4 ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Determine whether the function has an inverse function.If it does,find the inverse function. f(x)= x² + 5

Determine whether the function is one-to- one. Y = 3x

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. F(x)= |x - 9| + 1

Use the functions given by $f ( x ) = \frac { 1 } { 125 } x - 1$ and g(x)= x³ to find (f _º g)^-1. ?

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.? $g ( x ) = \frac { 4 - x } { 5 }$ ? ?

Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x)= x³ to find g^-1 _º f^-1. ?

?Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f^-1. ?? ?

Restrict the domain of f(x)= x² + 5 to x ≥ 0.Use a graphing utility to graph the function.

Find the inverse of the one-to-one function. y = 5x + 4 f ^-1(x)= __________

Use the functions given by f(x)= x + 6 and g(x)= 7x - 3 to find g^-1 _º f^-1. ?

Find the inverse of the one-to-one function. $y = \frac { 1 } { 8 x }$ f ^-1(x)= __________

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. G(x)= |x + 5| - |x - 5|

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ? F(x)= (x - 5)² ?

Find the inverse function of g(x)= x² - 3 informally. ?

Select the correct graph,showing f and g are inverse functions.? $f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }$ ?

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. F(x)= |x + 5|

Find the inverse function of f informally. ? F(x)= x⁴ ?