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

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

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

Question 4

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

Accepted Answer

The answer of Find the inverse of the one-to-one function.
​
y...

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

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

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

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.

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)

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. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = - x + 6 - 6 = - x$

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)  $f ^ { - 1 } ( x ) = 36 + x ^ { 2 } , 0 \leq x \leq 6$

Question 12

Does the function have an inverse function?​  ​

Accepted Answer

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.

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.

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

Question 16

Does the function have an inverse function?​  ​

Accepted Answer

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)  $\frac { - x - 3 } { 2 }$

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

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

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

Exam 9: Inverse Functions

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.? $f ( x ) = \sqrt { 7 x + 8 }$ ?

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. $f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$

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) . $\begin{array} { | r | l | l | l | l | l | l | } \hline x & - 3 & - 2 & 0 & 1 & 2 & 3 \\\hline f ( x ) & - 4 & - 2 & 2 & 4 & 6 & 8 \\\hline\end{array}$

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.? $g ( x ) = \frac { x } { 5 }$ ?

Find the inverse function of f informally. ? F(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 ?

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 ?

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 ?

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.? $g ( x ) = \frac { x } { 5 }$ ?