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Inverse Functions and Their Properties

Inverse Functions and Their Properties

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
HSF-BF.B.4C, HSF-BF.B.4A, HSF-BF.B.4D

Standards-aligned

Created by

Aiden Montgomery

FREE Resource

Standards-aligned

CCSS.HSF-BF.B.4C
,
CCSS.HSF-BF.B.4A
,
CCSS.HSF-BF.B.4D
The video tutorial explains how to find the inverse of a given function, determine its domain and range, and verify the results graphically. It begins by identifying the domain and range of the original function using interval notation. The process of finding the inverse function involves interchanging variables and solving the resulting equation. The tutorial also covers how to determine the domain and range of the inverse function and concludes with a graphical verification to ensure the function and its inverse are reflections across the line y = x.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding the inverse of a function?

Interchange x and y

Replace f(x) with y

Solve for x

Graph the function

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why must the expression under the square root be non-negative?

To ensure the result is real

To simplify the equation

To make the function continuous

To find the range

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the domain of the given function in interval notation?

[3/5, ∞)

(-∞, 3/5]

[0, ∞)

(-∞, 0]

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the range of the given function?

[3/5, ∞)

(-∞, 0]

(-∞, 3/5]

[0, ∞)

Tags

CCSS.HSF-BF.B.4A

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the inverse function of f(x) = √(5x - 3)?

5√(x - 3)

5x^2 - 3

(x^2 + 3)/5

√(x^2 + 3)

Tags

CCSS.HSF-BF.B.4C

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the domain of the inverse function?

(-∞, 3/5]

(-∞, 0]

[0, ∞)

[3/5, ∞)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the range of the inverse function?

[3/5, ∞)

(-∞, 3/5]

[0, ∞)

(-∞, 0]

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