Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
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 $f^{-1}(f(x)) = x$.
5 Must Know Facts For Your Next Test
The inverse of a function $f(x)$ is denoted as $f^{-1}(x)$.
To find an inverse function, swap the roles of $x$ and $y$ in the equation and solve for y.
A function must be one-to-one (bijective) to have an inverse.
Graphically, the graph of an inverse function is the reflection of the original function across the line $y = x$.
If a function passes the horizontal line test, it has an inverse.
A test used to determine if a function has an inverse by checking if any horizontal line intersects the graph more than once.
Bijective Function: A bijective function is both injective (one-to-one) and surjective (onto), meaning it maps every element of its domain to a unique element in its codomain.