AnswersPrecalculusInverse of a Function

Inverse of a Function — Quiz Answers

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1
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Marin writes the functions m times x is equal to the fraction with numerator 3 x and denominator x plus 7 and n times x is equal to the fraction with numerator 7 x and denominator 3 minus x Which equation must be true for m times x and n times x to be inverse functions?

A
the fraction with numerator 3 times open paren the fraction with numerator 7 x and denominator 3 minus x close paren and denominator open paren the fraction with numerator 7 x and denominator 3 minus x close paren plus 7 is equal to the fraction with numerator 7 times open paren the fraction with numerator 3 x and denominator x plus 7 close paren and denominator 3 minus open paren the fraction with numerator 3 x and denominator x plus 7 close paren is equal to x
B
the fraction with numerator 3 times open paren the fraction with numerator 3 x and denominator x plus 7 close paren and denominator open paren the fraction with numerator 3 x and denominator x plus 7 close paren plus 7 is equal to the fraction with numerator 7 times open paren the fraction with numerator 7 x and denominator 3 minus x close paren and denominator 3 minus open paren the fraction with numerator 7 x and denominator 3 minus x close paren is equal to 0
C
the fraction with numerator 3 times open paren the fraction with numerator 7 x and denominator 3 minus x close paren and denominator open paren the fraction with numerator 7 x and denominator 3 minus x close paren plus 7 is equal to the fraction with numerator 7 times open paren the fraction with numerator 3 x and denominator x plus 7 close paren and denominator 3 minus open paren the fraction with numerator 3 x and denominator x plus 7 close paren is equal to 0
D
the fraction with numerator 3 times open paren the fraction with numerator 3 x and denominator x plus 7 close paren and denominator open paren the fraction with numerator 3 x and denominator x plus 7 close paren plus 7 is equal to the fraction with numerator 7 times open paren the fraction with numerator 7 x and denominator 3 minus x close paren and denominator 3 minus open paren the fraction with numerator 7 x and denominator 3 minus x close paren is equal to x
2
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The table shows several points for function h of x x 0 3 6 9 12 15 h of x 1 6 12 2 8 9 Which point is on the graph of the inverse function h inverse of x ?

A
open paren 12 comma negative 18 close paren
B
open paren 0 comma 1 close paren
C
open paren 9 comma negative 15 close paren
D
open paren 6 comma 3 close paren
3

Given r times x is equal to the fraction with numerator 11 and denominator open paren x minus 4 close paren squared , which represents a domain restriction on r times x and the corresponding inverse function?

A
x is greater than negative 4 ; r inverse times x is equal to 4 minus square root of 11 over x end root
B
x is greater than 4 ; r inverse times x is equal to 4 plus square root of 11 over x end root
C
x is greater than negative 4 ; r inverse times x is equal to 4 plus square root of 11 over x end root
D
x is greater than 4 ; r inverse times x is equal to 4 minus square root of 11 over x end root
4

For the function k times x is equal to negative 1 over 16 x minus 8 , what is the inverse function k inverse times x ?

A
k inverse times x is equal to negative 16 times open paren x minus 8 close paren
B
k inverse times x is equal to negative 16 x plus 8
C
k inverse times x is equal to negative 16 x minus 8
D
k inverse times x is equal to negative 16 times open paren x plus 8 close paren
5

Manish writes the functions g of x is equal to cube root of negative x minus 72 and h of x is equal to negative open paren x plus 72 close paren cubed Which pair of expressions could Manish use to show that g of x and h of x are inverse functions?

A
cube root of negative x cubed minus 72 and negative open paren cube root of negative x plus 72 close paren cubed
B
cube root of x cubed minus 72 and negative open paren cube root of negative x plus 72 close paren cubed
C
cube root of negative open paren x plus 72 close paren cubed minus 72 and negative open paren cube root of negative x minus 72 plus 72 close paren cubed
D
cube root of open paren x plus 72 close paren cubed minus 72 and negative open paren cube root of negative x minus 72 plus 72 close paren cubed
6

For the constant function v times x is equal to 1 , which statement describes the additive and multiplicative inverses?

A
Neither inverse is equal to v times x .
B
Both inverses are equal to v times x .
C
The additive inverse is equal to v times x , but the multiplicative inverse is not.
D
The multiplicative inverse is equal to v times x , but the additive inverse is not.
7

For x is greater than 3 , values of the function f of x is equal to negative open paren x minus 3 close paren squared times open paren x plus 2 close paren are negative. On this same interval, which statement correctly describes the values of the additive and multiplicative inverses?

A
Both the additive inverse and the multiplicative inverse are negative.
B
Both the additive inverse and the multiplicative inverse are positive.
C
The additive inverse is negative, while the multiplicative inverse is positive.
D
The additive inverse is positive, while the multiplicative inverse is negative.
8

What are the additive and multiplicative inverses of h of x is equal to x minus 24 ?

A
additive inverse: j times x is equal to negative x plus 24 ; multiplicative inverse: k times x is equal to x plus 24
B
additive inverse: j times x is equal to x plus 24 ; multiplicative inverse: k times x is equal to the fraction with numerator 1 and denominator x minus 24
C
additive inverse: j times x is equal to the fraction with numerator 1 and denominator x minus 24 ; multiplicative inverse: k times x is equal to negative x plus 24
D
additive inverse: j times x is equal to negative x plus 24 ; multiplicative inverse: k times x is equal to the fraction with numerator 1 and denominator x minus 24
9

The table shows several points for function f of x x negative 4 negative 2 0 2 4 6 8 10 f of x 19 15 11 negative 6 negative 7 negative 8 negative 10 negative 14 Which statement correctly identifies a point on the graph of f inverse of x ?

A
The point open paren 4 comma negative 7 close paren is on the graph of f of x , so the point open paren 7 comma negative 4 close paren will be on the graph of f inverse of x .
B
The point open paren 10 comma negative 14 close paren is on the graph of f of x , so the point open paren negative 14 comma 10 close paren will be on the graph of f inverse of x .
C
The point open paren negative 2 comma 15 close paren is on the graph of f of x , so the point open paren 2 comma negative 15 close paren will be on the graph of f inverse of x .
D
The point open paren negative 4 comma 19 close paren is on the graph of f of x , so the point open paren negative 4 comma negative 19 close paren will be on the graph of f inverse of x .
10

Let q times t is equal to 29 t and r times t is equal to t over 29 Which method could be the first step in proving that q times t and r times t are inverse functions?

A
Replace the t in the expression for q times t with t over 29 , and replace the t in the expression for r times t with 29 t .
B
Replace the t in the expression for q times t with 29 t , and replace the t in the expression for r times t with t over 29 .
C
Replace the 29 t in the expression for q times t with t , and rplace the t over 29 in the expression for r times t with t .
D
Replace the 29 t in the expression for q times t with t over 29 , and replace the t over 29 in the expression for r times t with 29 t .

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