Question

For each function, a) determine whether it is one-to-one; b) if it is one-to-one, determine its inverse function. $f(x)=x-4$

Name: Problem 50, Chapter 9: Intermediate Algebra for College Students
Uploaded: 2020-07-29T17:01:03-08:00
Duration: 1 min 35 s
Channel: Ankit Gupta
Description: For each function, a) determine whether it is one-to-one; b) if it is one-to-one, determine its inverse function. f(x)=x-4

   For each function, a) determine whether it is one-to-one; b) if it is one-to-one, determine its inverse function.
$f(x)=x-4$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 9, Problem 50

Instant Answer

Solved by Expert Ankit Gupta

07/29/2020

Step 1

In other words, if $f(x_1) = f(x_2)$, then $x_1$ must equal $x_2$. Let's check this for the given function: $f(x_1) = x_1 - 4$ $f(x_2) = x_2 - 4$ If $f(x_1) = f(x_2)$, then: $x_1 - 4 = x_2 - 4$ Adding 4 to both sides, we get: $x_1 = x_2$ Since $x_1$ must Show more…

Show all steps

Thanks for your feedback!

For each function, a) determine whether it is one-to-one; b) if it is one-to-one, determine its inverse function. $f(x)=x-4$

Play audio

Feedback

Ankit Gupta and 75 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

One-to-One Functions

A function is one-to-one (or injective) if every distinct input maps to a distinct output. This property means that no two different inputs produce the same output, which is essential for ensuring that the function can have an inverse. Checking one-to-one-ness often involves analyzing the function's algebraic form or employing the horizontal line test graphically.

Inverse Functions

An inverse function reverses the effect of the original function, meaning it 'undoes' the mapping from inputs to outputs. To find the inverse, one typically swaps the roles of the input and output variables and then solves for the new output variable. Inverse functions only exist for one-to-one functions, highlighting the importance of injectivity in their determination.

Please give Ace some feedback