Question 1

Show algebraically that f and g are inverse functions.
f(x)= 9x + 9 $$g ( x ) = \frac { x - 9 } { 9 }$$

Accepted Answer

$f ( g ( x ) ) = f \left( \frac { x - 9 } { 9 } \right) = 9 \left( \frac { x - 9 } { 9 } \right) + 9 = x - 9 + 9 = x$ $g ( f ( x ) ) = g ( 9 x + 9 ) = \frac { 9 x + 9 - 9 } { 9 } = \frac { 9 x } { 9 } = x$

Question 2

Determine whether the function has an inverse function.If it does,find the inverse function.? $f ( x ) = \left\{ \begin{array} { l } 
x + 2 , x < 0 \
2 - x , x \geq 0
\end{array} $ ?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$. 
B)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$ 
C)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x - 2 , x \geq 0 \
2 + x , x < 0
\end{array} \right.$ 
D)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x + 2 , x \geq 0 \
2 - x , x < 0
\end{array} \right.$. 
E) No inverse 
A)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$. 
B)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$ 
C)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x - 2 , x \geq 0 \
2 + x , x < 0
\end{array} \right.$ 
D)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x + 2 , x \geq 0 \
2 - x , x < 0
\end{array} \right.$. 
E) No inverse E

Question 3

Determine algebraically whether f and g are inverse functions. f(x)= 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

Accepted Answer

A) Yes,f and g are inverse functions. $f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$ $g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = x$ 
B) No,f and g are not inverse functions. $f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$ $g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = - x$ 
A) Yes,f and g are inverse functions. $f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$ $g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = x$ 
B) No,f and g are not inverse functions. $f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$ $g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = - x$ A

Question 4

Find the inverse of the one-to-one function. ?
Y = 3x
?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = 3 x ^ { 2 }$ 
B) f -1(x)= 3x 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 3 } { x }$ 
E) f -1(x)= 9x 
A)  $f ^ { - 1 } ( x ) = 3 x ^ { 2 }$ 
B) f -1(x)= 3x 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 3 } { x }$ 
E) f -1(x)= 9x

Question 5

Determine whether the function is one-to-one. ​
Y = (x - 5)2;x ≥ 5
​

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 6

Select the graph of f and f-1 on the same set of coordinate axes. ​
F(x)= 2x - 3
​

Accepted Answer

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

Question 7

Show algebraically that f and g are inverse functions. $f ( x ) = \sqrt { x - 8 }$ ,x ≥ 8 g(x)= x2 + 8,x ≥ 0

Accepted Answer

Question 8

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = \frac { x - 1 } { x + 8 } , g ( x ) = - \frac { 8 x + 1 } { x - 1 }$$ ?

Accepted Answer

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

Question 9

Determine whether the function has an inverse function.If it does,find the inverse function. ?
G(x)= x7
?

Accepted Answer

A)  $g ^ { - 1 } ( x ) = \frac { 7 } { x }$ 
B) g-1(x)= -7x 
C) ? $$g ^ { - 1 } ( x ) = - \frac { x } { 7 }$$ 
D) g-1(x)= 7x 
E) The inverse exists,but none of the above 
A)  $g ^ { - 1 } ( x ) = \frac { 7 } { x }$ 
B) g-1(x)= -7x 
C) ? $$g ^ { - 1 } ( x ) = - \frac { x } { 7 }$$ 
D) g-1(x)= 7x 
E) The inverse exists,but none of the above

Question 10

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = 9 x , g ( x ) = \frac { x } { 9 }$$ ?

Accepted Answer

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

Question 11

Select the graph of f and f-1 on the same set of coordinate axes.? $$f ( x ) = \frac { 3 } { x }$$ ?

Accepted Answer

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

Question 12

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6$$ ?

Accepted Answer

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

Question 13

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

Accepted Answer

A) -2 
B) 0 
C) -4 
D) 2 
E) 4 
A) -2 
B) 0 
C) -4 
D) 2 
E) 4

Question 14

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

Accepted Answer

A) ? $- \frac { 387 } { 512 }$ 
B) ? $2 \sqrt [ 3 ] { 6 }$ 
C) ? $- 2 \sqrt [ 3 ] { 6 }$ 
D) ? $2 \sqrt [ 3 ] { 4 }$ 
E) ?Undefined 
A) ? $- \frac { 387 } { 512 }$ 
B) ? $2 \sqrt [ 3 ] { 6 }$ 
C) ? $- 2 \sqrt [ 3 ] { 6 }$ 
D) ? $2 \sqrt [ 3 ] { 4 }$ 
E) ?Undefined

Question 15

Find the inverse of the one-to-one function. ?
Y = 5x + 9
?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { x - 9 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 5 } { 9 }$ 
E) none of the above 
A)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { x - 9 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 5 } { 9 }$ 
E) none of the above

Question 16

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$$ ?

Accepted Answer

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

Question 17

Find the inverse of the one-to-one function.? $y = \frac { 1 } { 8 x }$ ?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 8 } { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 8 }$ 
C)  $f ^ { - 1 } ( x ) = 8 x$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { 8 x }$ 
E) inverse does not exist 
A)  $f ^ { - 1 } ( x ) = \frac { 8 } { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 8 }$ 
C)  $f ^ { - 1 } ( x ) = 8 x$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { 8 x }$ 
E) inverse does not exist

Question 18

Graph the given function. f(x)= (x - 3)2

Accepted Answer

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

Question 19

Consider the functions given by f(x)= x + 3 and f-1(x)= x - 3.Evaluate f(f-1(x))and f-1(f(x))for the indicated values of x.What can you conclude about the functions
$$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & & & & \
\hline f ^ { - 1 } ( f ( x ) ) & & & & \
\hline
\end{array}$$

Accepted Answer

A)  $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & - 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \
\hline
\end{array}$$We can conclude that, both the functions have the same value for negative variables 
B) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \
\hline
\end{array}$$We can conclude that, both the functions have the same value 
C) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & - 49 \
\hline
\end{array}$$We can conclude that, both the functions have the same value for negative variables. 
D) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & - 49 \
\hline
\end{array}$$We can conclude that, both the functions are opposite of each other. 
E) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & - 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & 49 \
\hline
\end{array}$$
We can conclude that, both the functions are opposite of each other. 
A)  $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & - 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \
\hline
\end{array}$$We can conclude that, both the functions have the same value for negative variables 
B) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \
\hline
\end{array}$$We can conclude that, both the functions have the same value 
C) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & - 49 \
\hline
\end{array}$$We can conclude that, both the functions have the same value for negative variables. 
D) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & - 49 \
\hline
\end{array}$$We can conclude that, both the functions are opposite of each other. 
E) $$\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & 0 & 4 & 49 \
\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & - 49 \
\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & 49 \
\hline
\end{array}$$
We can conclude that, both the functions are opposite of each other.

Question 20

The function given by y = 0.03x2 + 245.50,0 < x < 100 approximates the exhaust temperature y in degrees Fahrenheit,x where is the percent load for a diesel engine.Find the inverse function. ?

Accepted Answer

A)  $y = \frac { x + 245.50 } { - 0.03 }$ 
B)  $y = \sqrt { \frac { x - 245.50 } { 0.03 } }$ 
C)  $y = \frac { x - 245.50 } { 0.03 }$ 
D)  $y = \sqrt { \frac { x + 245.50 } { 0.03 } }$ 
E)  $y = \frac { x + 245.50 } { 0.03 }$ 
A)  $y = \frac { x + 245.50 } { - 0.03 }$ 
B)  $y = \sqrt { \frac { x - 245.50 } { 0.03 } }$ 
C)  $y = \frac { x - 245.50 } { 0.03 }$ 
D)  $y = \sqrt { \frac { x + 245.50 } { 0.03 } }$ 
E)  $y = \frac { x + 245.50 } { 0.03 }$

Exam 9: Inverse Functions

Show algebraically that f and g are inverse functions. f(x)= 9x + 9 g(x)=x−99g ( x ) = \frac { x - 9 } { 9 }g(x)=9x−9​

Determine whether the function has an inverse function.If it does,find the inverse function.? \(f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\ 2 - x , x \geq 0 \end{array} \\) ?

Determine algebraically whether f and g are inverse functions. f(x)= 5x - 3 g(x)=x+35g ( x ) = \frac { x + 3 } { 5 }g(x)=5x+3​

Find the inverse of the one-to-one function. ? Y = 3x ?

Determine whether the function is one-to-one. ​ Y = (x - 5)2;x ≥ 5 ​

Select the graph of f and f-1 on the same set of coordinate axes. ​ F(x)= 2x - 3 ​

Show algebraically that f and g are inverse functions. f(x)=x−8f ( x ) = \sqrt { x - 8 }f(x)=x−8​ ,x ≥ 8 g(x)= x2 + 8,x ≥ 0

Select the correct graph,showing f and g are inverse functions.? f(x)=x−1x+8,g(x)=−8x+1x−1f ( x ) = \frac { x - 1 } { x + 8 } , g ( x ) = - \frac { 8 x + 1 } { x - 1 }f(x)=x+8x−1​,g(x)=−x−18x+1​ ?

Determine whether the function has an inverse function.If it does,find the inverse function. ? G(x)= x7 ?

Select the correct graph,showing f and g are inverse functions.? f(x)=9x,g(x)=x9f ( x ) = 9 x , g ( x ) = \frac { x } { 9 }f(x)=9x,g(x)=9x​ ?

Select the graph of f and f-1 on the same set of coordinate axes.? f(x)=3xf ( x ) = \frac { 3 } { x }f(x)=x3​ ?

Select the correct graph,showing f and g are inverse functions.? f(x)=6−x2,g(x)=6−x,x≤6f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6f(x)=6−x2,g(x)=6−x​,x≤6 ?

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 (g-1 º f-1)(-5). ?

?Use the functions given by f(x)=x8−1f ( x ) = \frac { x } { 8 } - 1f(x)=8x​−1 and g(x)= x3 to find the indicated value. (f º g)-1(5)

Find the inverse of the one-to-one function. ? Y = 5x + 9 ?

Select the correct graph,showing f and g are inverse functions.? f(x)=6x+1,g(x)=x−16f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }f(x)=6x+1,g(x)=6x−1​ ?

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

Graph the given function. f(x)= (x - 3)2

Consider the functions given by f(x)= x + 3 and f-1(x)= x - 3.Evaluate f(f-1(x))and f-1(f(x))for the indicated values of x.What can you conclude about the functions x -1 0 4 49 f (x) (f(x))

The function given by y = 0.03x2 + 245.50,0 < x < 100 approximates the exhaust temperature y in degrees Fahrenheit,x where is the percent load for a diesel engine.Find the inverse function. ?

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Show algebraically that f and g are inverse functions. f(x)= 9x + 9 $g ( x ) = \frac { x - 9 } { 9 }$

Determine algebraically whether f and g are inverse functions. f(x)= 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

Determine whether the function is one-to-one. Y = (x - 5)²;x ≥ 5

Select the graph of f and f^-1 on the same set of coordinate axes. F(x)= 2x - 3

Show algebraically that f and g are inverse functions. $f ( x ) = \sqrt { x - 8 }$ ,x ≥ 8 g(x)= x² + 8,x ≥ 0

Select the correct graph,showing f and g are inverse functions.? $f ( x ) = \frac { x - 1 } { x + 8 } , g ( x ) = - \frac { 8 x + 1 } { x - 1 }$ ?

Determine whether the function has an inverse function.If it does,find the inverse function. ? G(x)= x⁷ ?

Select the correct graph,showing f and g are inverse functions.? $f ( x ) = 9 x , g ( x ) = \frac { x } { 9 }$ ?

Select the graph of f and f^-1 on the same set of coordinate axes.? $f ( x ) = \frac { 3 } { x }$ ?

Select the correct graph,showing f and g are inverse functions.? $f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6$ ?

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

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

Select the correct graph,showing f and g are inverse functions.? $f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$ ?

Find the inverse of the one-to-one function.? $y = \frac { 1 } { 8 x }$ ?

Graph the given function. f(x)= (x - 3)²

Consider the functions given by f(x)= x + 3 and f^-1(x)= x - 3.Evaluate f(f^-1(x))and f^-1(f(x))for the indicated values of x.What can you conclude about the functions x -1 0 4 49 f (x) (f(x))

The function given by y = 0.03x² + 245.50,0 < x < 100 approximates the exhaust temperature y in degrees Fahrenheit,x where is the percent load for a diesel engine.Find the inverse function. ?