College Algebra

study guides for every class

that actually explain what's on your next test

Inverse function

from class:

College Algebra

Definition

An inverse function reverses the operation of a given function. If $f(x)$ is a function, its inverse $f^{-1}(x)$ satisfies $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$.

congrats on reading the definition of inverse function. now let's actually learn it.

ok, let's learn stuff

5 Must Know Facts For Your Next Test

  1. The inverse of a function $f(x)$ is denoted as $f^{-1}(x)$.
  2. To find an inverse function, swap the roles of $x$ and $y$ in the equation and solve for y.
  3. A function must be one-to-one (bijective) to have an inverse.
  4. Graphically, the graph of an inverse function is the reflection of the original function across the line $y = x$.
  5. If a function passes the horizontal line test, it has an inverse.

Review Questions

  • What is the notation for an inverse function?
  • Describe how you would find the inverse of a given function algebraically.
  • How can you use graphs to determine if a function has an inverse?
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides