Inverse Function Checker

Determine if a function has an inverse using the derivative test. Just enter your function f(x).

Enter Function f(x):

f(x) =

Result

Derivative of f(x):

Inverse Function Exists?

What is an Inverse Function?

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function. If a function f takes an input x and produces an output y, then the inverse function, denoted as f⁻¹(y), takes y as an input and produces x as an output. In simpler terms, if f(x) = y, then f⁻¹(y) = x.

Horizontal Line Test: A function has an inverse if and only if no horizontal line intersects its graph more than once. This means that for every y-value, there is at most one x-value that corresponds to it.

Derivative Test: For differentiable functions, if the derivative f'(x) is always positive or always negative over the domain of the function, then the function is strictly monotonic (either strictly increasing or strictly decreasing) and thus has an inverse. This tool uses this derivative test to check for the existence of an inverse function.

Learn more about inverse functions on Wikipedia.