Comparing a Function and Its Inverse — Quiz

Question 1

Consider the function and its inverse. f of x is equal to x squared plus 4 and f inverse of x is equal to negative square root of x minus 4 end root When comparing the functions using the equations, which conclusion can be made?

Revolt · Accepted Answer

The domain of f of x is restricted to x is less than or equal to 0 , and the domain of f inverse of x is restricted to x is greater than or equal to 4 .

Question 2

Consider the function. f of x is equal to 2 and 1 half minus 3 and 1 third x What is the x -intercept of f inverse of x ?

Revolt · Accepted Answer

open paren 2 and 1 half comma 0 close paren

Question 3

Students are asked to graph the inverse, f inverse of x of an absolute value function, f of x after restricting its domain. The directions also ask that the graph include a dashed line that can be used to verify that the functions are inverses of each other. Which student’s work is correct?

Revolt · Accepted Answer

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma 1) and goes through (6 comma 7). The line (f inverse of x) originates from (1 comma 0) and goes through (7 comma 6). A dashed line with a positive slope passes through (0 comma 0) and (7 comma 7).

Question 4

Which answer pairs a possible domain restriction for f of x and its corresponding impact on f inverse of x ?

Revolt · Accepted Answer

f of x domain: x is greater than or equal to 1 f inverse of x range: y is greater than or equal to 1

Question 5

A linear function and its inverse are given. y is equal to 4 x minus 3 and y is equal to 1 fourth x plus 3 fourths Which tables could be used to verify that the functions are inverses of each other? Choose two correct answers.

Revolt · Accepted Answer

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 23'; Column 3, 'negative 15'; Column 4, 'negative 3'; Column 5, '1'; Column 6, '13' Row 2: Column 1, 'y'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '1'; Column 6, '4'; Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '1'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, 'negative 23'; Column 3, 'negative 15'; Column 4, 'negative 3'; Column 5, '1'; Column 6, '13'

Question 6

Which explanation could be used to verify whether the functions are inverses?

Revolt · Accepted Answer

The point of intersection of the two functions is not on the line y is equal to x ; therefore, the functions are not inverses of each other.

Question 7

Which table could be used with Table A to verify that the function modeling Fahrenheit temperature, degree cap f cap c , based on a given Celsius temperature, degree cap c , is the inverse of degree cap c cap f ?

Revolt · Accepted Answer

Table with 4 columns and 2 rows.Row 1: Column 1, 'degree cap c'; Column 2, 'negative 20'; Column 3, 'negative 15'; Column 4, 'negative 5' Row 2: Column 1, 'degree cap c cap f'; Column 2, 'negative 4'; Column 3, '5'; Column 4, '23'

Question 8

When verifying that a function represented in another table is the inverse of the given cost function, which ordered pair can be expected?

Revolt · Accepted Answer

open paren 52 comma 20 close paren

Comparing a Function and Its Inverse — Quiz Answers

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