Answers2026-2027_MDCPS_1200330_Algebra 2_FYFunction Inverses

Function Inverses — Unit test Answers

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For which pair of functions is ?

Question illustration
A
f(x) = 3 – 4x and g(x) = 16x – 3
B
f(x) = 6x2 and
Option B
C
and g(x) = 144x
Option C
D
f(x) = 4x and g(x) = 3x
2
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Which statement verifies that f(x) and g(x) are inverses of each other?

A
Option
Option A
B
and
Option B
C
Option
Option C
D
and
Option D
3

Rami is solving the equation for x .–6x – 1 = 5–6x – 1 1 = (5 1)–6x = 6–6x – 6 = 6 –6x = –1

Question illustration
A
should contain +; should contain ×
Option A
B
should contain +; should contain ÷
Option B
C
should contain –; should contain ×
Option C
D
should contain –; should contain ÷
Option D
4

If and , what is the degree of ?

Question illustration
A
2
B
3
C
5
D
6
5

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of ?

Question illustration
A
all real values of x
B
all real values of x except x = 5
C
all real values of x except x = –5
D
all real values of x except x = 5 and x = –5
6

The graph of f(x) is shown below.If g(x) and f(x) are inverse functions, which graph represents g(x)?

Question illustration
A
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up sharply through (2, 4).
Option A
B
On a coordinate plane, a curve opens down and to the left in quadrant 2. The curve starts at (0, 0) and gradually curves through (negative 4, 2).
Option B
C
On a coordinate plane, a curve opens open and to the left in quadrant 3. The curve starts at (0, 0) and curves gradually through (negative 4, negative 2).
Option C
D
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up through (4, 1).
Option D
7

The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of ?

Question illustration
A
u(x) 0 and v(x) 2
Option A
B
x 0 and x cannot be any value for which u(x) 2
Option B
C
x 2 and x cannot be any value for which v(x) 0
Option C
D
u(x) 2 and v(x) 0
Option D
8

If the function has an inverse function, which statement must be true?

Question illustration
A
b not-equals 0
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Mr. Valenzuela’s new bottle of shampoo contains 60 ounces of shampoo. He uses ounce of shampoo each time he washes his hair. Which equation can be used to find x, the number of washes after which 24 ounces will remain in the bottle?

Question illustration
A
One-fourth x minus 60 equals 24
Option A
B
60 minus one-fourth x equals 24
Option B
C
One-fourth x minus 24 equals 60
Option C
D
24 minus one-fourth x equals 60
Option D
10

Which function is the inverse of ?

Question illustration
A
f Superscript negative 1 Baseline (x) = negative one-fifth x + four-fifths
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

If r(x) = 2 – x2 and w(x) = x – 2, what is the range of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

The equation |p| = 2 represents the total number of points that can be earned or lost during one turn of a game. Which best describes how many points can be earned or lost during one turn?

A
–2
B
2
C
0 or 2
D
–2 or 2
13

The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?

A
14x – 8
B
14x + 4
C
4x – 8
D
4x + 4
14

The tables for f(x) and g(x) are shown below.xf(x)–5–11–21113529xg(x)–5–7–2–115513What is the value of (f – g)(5)?

A
–18
B
–4
C
16
D
42
15

Katie ordered candles that cost $3 each from a website. She was charged a flat shipping fee of $6 and no sales tax. If she spent a total of $54, which equation can be used to find c, the number of candles she ordered?

A
3c = 54
B
6c = 54
C
3c + 6 = 54
D
3c – 6 = 54

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