AnswersGA-GSE Pre-CalculusComparing a Function and Its Inverse

Comparing a Function and Its Inverse Answers

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1
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A function and its inverse are shown on the graph.

Question illustration
A
The range of both f(x) and f–1(x) is all real numbers.
B
The domain of both f(x) and f–1(x) is all real numbers.
C
The range of f(x) is y > 0 and the domain of f–1(x) is x > 0.
D
The domain of f(x) is x > 0 and the range of f–1(x) is y > 0.
2
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Consider the function.What is the y-intercept of f–1(x)?

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A
–16
B
–12
C
Option
Option C
D
Option
Option D
3

Consider the tables that represent ordered pairs corresponding to a function and its inverse.

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A
According to the tables, f(x) does not have a y-intercept.
B
According to the tables, f–1(x) does not have an x-intercept.
C
The domain of f(x) is restricted such that x ≥ 0, so the domain of f–1(x) is restricted such that y ≥ 0.
D
The range of f(x) includes values such that y ≥ 1, so the domain of f–1(x) includes values such that x ≥ 1.
4

A linear function and its inverse are given. Which tables could be used to verify that the functions are inverses of each other? Select two options.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
E
Option
Option E
5

Consider the function.What is the x-intercept of f–1(x)?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

The graph below shows two linear functions.

Question illustration
A
Neither of the lines is parallel to the line y = x; therefore, the functions are inverses of each other.
B
Neither of the lines is parallel to the line y = x; therefore, the functions are not inverses of each other.
C
The point of intersection of the two functions is not on the line y = x; therefore, the functions are inverses of each other.
D
The point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.
7

The cost table shows the average cost, a(x), of producing x number of earbuds.

Question illustration
A
(20, 20)
B
(52, 20)
C
(20, 52)
D
(52, 52)
8

Table A represents the function that models the stopping distance in feet of a derby car, d(x), based on the velocity in miles per hour of the car, x.Table B represents the function that models the velocity of a car, v(d), in miles per hour based on distance in feet it took the car to stop, d.

Question illustration
A
Since the functions in both tables are increasing, they are inverses.
B
Since the functions in both tables are increasing, they are not inverses.
C
Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are inverses.
D
Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are not inverses.
9

A function and its inverse are shown on the graph.

Question illustration
A
f(x) domain: x ≥ 1f–1(x) domain: x ≥ 1
B
f(x) domain: x ≥ 1f–1(x) range: y ≥ 1
C
f(x) domain: x ≤ –2f–1(x) domain: x ≤ –2
D
f(x) domain: x ≤ –2f–1(x) range: y ≤ –2
10

Consider the function and its inverse. and When comparing the functions using the equations, which conclusion can be made?

Question illustration
A
The domain of f(x) is restricted to x ≥ 0, and the domain of f–1(x) is restricted to x ≥ 0.
B
The domain of f(x) is restricted to x ≥ 0, and the domain of f–1(x) is restricted to x ≤ 0.
C
The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≥ 4.
D
The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≤ 4.

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