Question 1

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x)= x3 to find (f-1 º f-1)(-5). ?

Accepted Answer

A) 36 
B) 44 
C) 40 
D) 38 
E) 42 
A) 36 
B) 44 
C) 40 
D) 38 
E) 42

Question 2

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 1$ and g(x)= x3 to find (f-1 º g-1)(1). ?

Accepted Answer

A) 14 
B) 12 
C) 16 
D) 20 
E) 18 
A) 14 
B) 12 
C) 16 
D) 20 
E) 18

Question 3

Determine whether the function has an inverse function.If it does,find the inverse function. ?
F(x)= (x + 4)2,x ? -4
?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x } + 4$ 
B) f-1(x)= -(x + 4)2 
C) f-1(x)= (x + 4)-2 
D) ? $f ^ { - 1 } ( x ) = \sqrt { x } - 4$ 
E) No inverse 
A)  $f ^ { - 1 } ( x ) = \sqrt { x } + 4$ 
B) f-1(x)= -(x + 4)2 
C) f-1(x)= (x + 4)-2 
D) ? $f ^ { - 1 } ( x ) = \sqrt { x } - 4$ 
E) No inverse

Question 4

Find the inverse of the one-to-one function.
​
y = 6x
​
f -1(x)= __________

Accepted Answer

Question 5

The function f(x)= x2 - 2 is one-to-one on the domain (x ? 0).Find f -1(x). ?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \sqrt { x + 2 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 2 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 2 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x - 2 }$ 
E) f -1(x)= x2 + 2 
A)  $f ^ { - 1 } ( x ) = - \sqrt { x + 2 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 2 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 2 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x - 2 }$ 
E) f -1(x)= x2 + 2

Question 6

Determine whether the function has an inverse function.If it does,find the inverse function.? $f ( x ) = \sqrt { 7 x + 8 }$ ?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } + 8 } { 7 }$ 
B)  $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } - 8 } { 7 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } - 8 } { 7 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } + 8 } { 7 }$ 
E) No Inverse 
A)  $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } + 8 } { 7 }$ 
B)  $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } - 8 } { 7 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } - 8 } { 7 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } + 8 } { 7 }$ 
E) No Inverse

Question 7

Find the inverse function of f informally. ?
F(x)= 6x
?

Accepted Answer

A) f-1(x)= 6 - x 
B) f-1(x)= 6 + x 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 6 } x$ 
D) f-1(x)= x - 6 
E) f(x)= 6x 
A) f-1(x)= 6 - x 
B) f-1(x)= 6 + x 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 6 } x$ 
D) f-1(x)= x - 6 
E) f(x)= 6x

Question 8

Determine whether the function has an inverse function.If it does,find the inverse function. $f ( x ) = \left\{ \begin{array} { l } 
8 x + 13 , x < - 2 \
( x + 2 ) ^ { 2 } - 3 , x \geq - 2
\end{array} \right.$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 2 \\
\sqrt { x + 3 } - 2 , x \geq - 2
\end{array} \right.$ 
B) ? $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { c } 
\frac { x - 13 } { 8 } , x < - 2 \\
\sqrt { x + 1 } , x \geq - 2
\end{array} \right.$$ 
C)  $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 3 \\
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$$ 
D)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x + 13 } { 8 } , x < - 3 \\
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$ 
E) No inverse function exists. 
A)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 2 \\
\sqrt { x + 3 } - 2 , x \geq - 2
\end{array} \right.$ 
B) ? $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { c } 
\frac { x - 13 } { 8 } , x < - 2 \\
\sqrt { x + 1 } , x \geq - 2
\end{array} \right.$$ 
C)  $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 3 \\
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$$ 
D)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x + 13 } { 8 } , x < - 3 \\
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$ 
E) No inverse function exists.

Question 9

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0$$ ?

Accepted Answer

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

Question 10

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x)= x2 - 6,x ? 0

Accepted Answer

A) Yes,f and g are inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = x + 6 - 6 = x$ 
B) No,f and g are not inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = - x + 6 - 6 = - x$ 
A) Yes,f and g are inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = x + 6 - 6 = x$ 
B) No,f and g are not inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = - x + 6 - 6 = - x$

Question 11

Find the inverse function of $f ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$ . ?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } - 36 } , 0 \leq x \leq 6$ 
C)  $f ^ { - 1 } ( x ) = 36 - x ^ { 2 } , 0 \leq x \leq 6$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { 36 + x ^ { 2 } } , 0 \leq x \leq 6$ 
E)  $f ^ { - 1 } ( x ) = 36 + x ^ { 2 } , 0 \leq x \leq 6$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } - 36 } , 0 \leq x \leq 6$ 
C)  $f ^ { - 1 } ( x ) = 36 - x ^ { 2 } , 0 \leq x \leq 6$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { 36 + x ^ { 2 } } , 0 \leq x \leq 6$ 
E)  $f ^ { - 1 } ( x ) = 36 + x ^ { 2 } , 0 \leq x \leq 6$

Question 12

Does the function have an inverse function?​   ​

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

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.? $$g ( x ) = - 2 x \sqrt { 6 - x ^ { 2 } }$$ ? ?

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)= -6x2 + 2
?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ 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 ? 2.? 
B)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 2 ( x - 6 ) } } { 2 }$ 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 ? 2.? 
C)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { - 6 }$ 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 ? 2.? 
D)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ 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 ? -2.? 
E)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x + 2 ) } } { 6 }$ 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 ? 2. 
A)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ 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 ? 2.? 
B)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 2 ( x - 6 ) } } { 2 }$ 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 ? 2.? 
C)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { - 6 }$ 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 ? 2.? 
D)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ 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 ? -2.? 
E)  $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x + 2 ) } } { 6 }$ 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 ? 2.

Question 15

Use the tables of values for y = f(x)to complete a table for y = f -1(x). 
$$\begin{array} { | r | l | l | l | l | l | l | } 
\hline x & - 3 & - 2 & 0 & 1 & 2 & 3 \
\hline f ( x ) & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline
\end{array}$$

Accepted Answer

A) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 1 & 8 & 3 \
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 6 \
\hline f ^ { - 1 } ( x ) & - 2 & - 2 & 0 & 1 & 2 & 3 \
\hline
\end{array}$$ 
C) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & 0 & 1 & 1 & 8 & 3 \
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 6 & 2 & 3 \
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 1 & 2 & 3 \
\hline
\end{array}$$ 
A) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 1 & 8 & 3 \
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 6 \
\hline f ^ { - 1 } ( x ) & - 2 & - 2 & 0 & 1 & 2 & 3 \
\hline
\end{array}$$ 
C) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & 0 & 1 & 1 & 8 & 3 \
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 6 & 2 & 3 \
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \
\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 1 & 2 & 3 \
\hline
\end{array}$$

Question 16

Does the function have an inverse function?​   ​

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 17

Use the functions given by f(x)= x + 2 and g(x)= 2x - 5 to find (f º g)-1. ?

Accepted Answer

A)  $\frac { x + 3 } { 2 }$ 
B)  $\frac { x - 3 } { - 2 }$ 
C)  $\frac { x - 4 } { 3 }$ 
D)  $\frac { x - 3 } { 2 }$ 
E)  $\frac { - x - 3 } { 2 }$ 
A)  $\frac { x + 3 } { 2 }$ 
B)  $\frac { x - 3 } { - 2 }$ 
C)  $\frac { x - 4 } { 3 }$ 
D)  $\frac { x - 3 } { 2 }$ 
E)  $\frac { - x - 3 } { 2 }$

Question 18

Determine whether the function has an inverse function.If it does,find the inverse function.? $h ( x ) = - \frac { 4 } { x ^ { 2 } }$ ?

Accepted Answer

A)  $h ^ { - 1 } ( x ) = \frac { 4 } { x ^ { 2 } }$ 
B)  $h ^ { - 1 } ( x ) = - \frac { x ^ { 2 } } { 4 }$ 
C)  $h ^ { - 1 } ( x ) = - \frac { 4 } { x ^ { 2 } }$ 
D)  $h ^ { - 1 } ( x ) = \frac { x ^ { 2 } } { 4 }$ 
E) No inverse 
A)  $h ^ { - 1 } ( x ) = \frac { 4 } { x ^ { 2 } }$ 
B)  $h ^ { - 1 } ( x ) = - \frac { x ^ { 2 } } { 4 }$ 
C)  $h ^ { - 1 } ( x ) = - \frac { 4 } { x ^ { 2 } }$ 
D)  $h ^ { - 1 } ( x ) = \frac { x ^ { 2 } } { 4 }$ 
E) No inverse

Question 19

Determine whether the function has an inverse function.If it does,find the inverse function.? $g ( x ) = \frac { x } { 5 }$ ?

Accepted Answer

A)  $g ^ { - 1 } ( x ) = - 5 x$ 
B)  $g ^ { - 1 } ( x ) = 5 x$ 
C)  $$g ^ { - 1 } ( x ) = \frac { 5 } { x }$$ 
D)  $g ^ { - 1 } ( x ) = - \frac { x } { 5 }$ 
E) No inverse 
A)  $g ^ { - 1 } ( x ) = - 5 x$ 
B)  $g ^ { - 1 } ( x ) = 5 x$ 
C)  $$g ^ { - 1 } ( x ) = \frac { 5 } { x }$$ 
D)  $g ^ { - 1 } ( x ) = - \frac { x } { 5 }$ 
E) No inverse

Question 20

Find the inverse function of f informally. ?
F(x)= x - 5
?

Accepted Answer

A) f-1(x)= - (x + 5) 
B) ? $f ^ { - 1 } ( x ) = \frac { 5 } { x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 5 }$ 
D) f-1(x)= 5 - x 
E) f-1(x)= x + 5 
A) f-1(x)= - (x + 5) 
B) ? $f ^ { - 1 } ( x ) = \frac { 5 } { x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 5 }$ 
D) f-1(x)= 5 - x 
E) f-1(x)= x + 5

Exam 9: Inverse Functions

Use the functions given by f(x)=18x−5f ( x ) = \frac { 1 } { 8 } x - 5f(x)=81​x−5 and g(x)= x3 to find (f-1 º f-1)(-5). ?

Use the functions given by f(x)=18x−1f ( x ) = \frac { 1 } { 8 } x - 1f(x)=81​x−1 and g(x)= x3 to find (f-1 º g-1)(1). ?

Determine whether the function has an inverse function.If it does,find the inverse function. ? F(x)= (x + 4)2,x ? -4 ?

Find the inverse of the one-to-one function. ​ y = 6x ​ f -1(x)= __________

The function f(x)= x2 - 2 is one-to-one on the domain (x ? 0).Find f -1(x). ?

Determine whether the function has an inverse function.If it does,find the inverse function.? f(x)=7x+8f ( x ) = \sqrt { 7 x + 8 }f(x)=7x+8​ ?

Find the inverse function of f informally. ? F(x)= 6x ?

Determine whether the function has an inverse function.If it does,find the inverse function. f(x)={8x+13,x<−2(x+2)2−3,x≥−2f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.f(x)={8x+13,x<−2(x+2)2−3,x≥−2​

Select the correct graph,showing f and g are inverse functions.? f(x)=x−3,g(x)=x2+3,x≥0f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0f(x)=x−3​,g(x)=x2+3,x≥0 ?

Determine algebraically whether f and g are inverse functions. f(x)=x+6f ( x ) = \sqrt { x + 6 }f(x)=x+6​ g(x)= x2 - 6,x ? 0

Find the inverse function of f(x)=36−x2,0≤x≤6f ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6f(x)=36−x2​,0≤x≤6 . ?

Does the function have an 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)=−2x6−x2g ( x ) = - 2 x \sqrt { 6 - x ^ { 2 } }g(x)=−2x6−x2​ ? ?

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)= -6x2 + 2 ?

Use the tables of values for y = f(x)to complete a table for y = f -1(x). x -3 -2 0 1 2 3 f(x) -4 -2 2 4 6 8

Does the function have an inverse function?​ ​

Use the functions given by f(x)= x + 2 and g(x)= 2x - 5 to find (f º g)-1. ?

Determine whether the function has an inverse function.If it does,find the inverse function.? h(x)=−4x2h ( x ) = - \frac { 4 } { x ^ { 2 } }h(x)=−x24​ ?

Determine whether the function has an inverse function.If it does,find the inverse function.? g(x)=x5g ( x ) = \frac { x } { 5 }g(x)=5x​ ?

Find the inverse function of f informally. ? F(x)= x - 5 ?

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

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x)= x³ to find (f^-1 _º f^-1)(-5). ?

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 1$ and g(x)= x³ to find (f^-1 _º g^-1)(1). ?

Determine whether the function has an inverse function.If it does,find the inverse function. ? F(x)= (x + 4)²,x ? -4 ?

Find the inverse of the one-to-one function. y = 6x f ^-1(x)= __________

The function f(x)= x² - 2 is one-to-one on the domain (x ? 0).Find f ^-1(x). ?

Determine whether the function has an inverse function.If it does,find the inverse function.? $f ( x ) = \sqrt { 7 x + 8 }$ ?

Determine whether the function has an inverse function.If it does,find the inverse function. $f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$

Select the correct graph,showing f and g are inverse functions.? $f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0$ ?

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x)= x² - 6,x ? 0

Find the inverse function of $f ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$ . ?

Does the function have an 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.? $g ( x ) = - 2 x \sqrt { 6 - x ^ { 2 } }$ ? ?

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)= -6x² + 2 ?

Use the tables of values for y = f(x)to complete a table for y = f ^-1(x). x -3 -2 0 1 2 3 f(x) -4 -2 2 4 6 8

Does the function have an inverse function?

Use the functions given by f(x)= x + 2 and g(x)= 2x - 5 to find (f _º g)^-1. ?

Determine whether the function has an inverse function.If it does,find the inverse function.? $h ( x ) = - \frac { 4 } { x ^ { 2 } }$ ?

Determine whether the function has an inverse function.If it does,find the inverse function.? $g ( x ) = \frac { x } { 5 }$ ?