Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

5 Questions

3 Views

Inverse Functions Quiz

Created by

@PortablePolarBear7499

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the inverse of function f given by $f = ig{(-2, 0), (0, 1), (2, 3), (3, 4)ig}$?

$f^{-1} = ig\{(0, -2), (1, 0), (2, 3), (3, 4)ig\}$

$f^{-1} = ig\{(-2, 0), (0, 1), (3, 2), (4, 3)ig\}$

$f^{-1} = ig\{(-2, 0), (1, 0), (2, 3), (4, 3)ig\}$

$f^{-1} = ig\{(0, -2), (1, 0), (3, 2), (4, 3)ig\}$ (correct)

What is the domain and range of the inverse of function f?

Domain: $(0, 1, 3, 4)$, Range: $(0, 1, 3, 4)$ (correct)

Domain: $(-2, 0, 2, 3)$, Range: $(0, 1, 3, 4)$

Domain: $(-2, 0, 2, 3)$, Range: $(-2, 0, 2, 3)$

Domain: $(0, 1, 3, 4)$, Range: $(-2, 0, 2, 3)$

Evaluate $f(f^{-1}(1))$ for the given functions.

$f(f^{-1}(1)) = 0$

$f(f^{-1}(1)) = -2$

$f(f^{-1}(1)) = 2$

$f(f^{-1}(1)) = 1$ (correct)

What are the properties of the graph of function $f$ and its inverse $f^{-1}$?

<p>They are reflections of each other over the line $y = x$</p> Signup and view all the answers

What is $f^{-1}(f(2))$ for the given functions?

<p>$f^{-1}(f(2)) = 2$</p> Signup and view all the answers

Study Notes

Inverse of Function f

The inverse of function f is denoted by f^(-1)
f^(-1) is found by swapping the x and y values in the given points: f^(-1) = {(0, -2), (1, 0), (3, 2), (4, 3)}

Domain and Range of Inverse of Function f

Domain of f^(-1) is the range of f: {-2, 0, 2, 3}
Range of f^(-1) is the domain of f: {0, 1, 3, 4}

Evaluating f(f^(-1)(1))

To evaluate f(f^(-1)(1)), first find f^(-1)(1) = 0
Then, f(f^(-1)(1)) = f(0) = 1

Properties of Graph of Function f and its Inverse f^(-1)

The graphs of f and f^(-1) are reflections of each other over the line y = x
The domain of f is the range of f^(-1) and vice versa
The range of f is the domain of f^(-1) and vice versa

Evaluating f^(-1)(f(2))

To evaluate f^(-1)(f(2)), first find f(2) = 3
Then, f^(-1)(f(2)) = f^(-1)(3) = 2

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of inverse functions with this quiz. Explore questions related to ordered pairs, linear, cubic root, square root, logarithmic, and exponential functions, along with detailed solutions. Practice algebraically and graphically checking answers using the properties of each function and its inverse. Strengthen your skills in solving inverse function problems step by step.