Question

If a function , what is its inverse function?

Ask by King Hart. in the United States
Dec 28,2024

Upstudy AI Solution

Tutor-Verified Answer

Answer

The inverse function of is .

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

To find the inverse function, start by replacing with : . Now, swap and , giving you . Then, solve for : subtract 2 from both sides, resulting in , and finally divide by 3: . So the inverse function is .
Interestingly, inverse functions can often be visualized as reflections over the line . If you graph and its inverse , you’ll see that they create a perfect mirror image along that line. This demonstrates how every input-output pair in one function corresponds to an output-input pair in its inverse!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy