Inverse function examples and solutions

Inverse Functions are an important concept in mathematics. An inverse function basically reverses the effect of the original function.

If you apply a function to a number and then apply its inverse, you get back the original number. For example, if a function turns 2 into 5, the inverse function will turn 5 back into 2.

In this article, we will learn about the inverse function, the conditions for the inverse function, and their properties and uses in detail.

What are Inverse Functions in Maths?

If functions f(x) and g(x) are inverses of each other, then f(x) = y only if g(y) = x. 

g(f(x)) = x

The figure given below describes a function and its inverse.

How to find the inverse of a function

This function is represented as f(x) and takes some input values and gives an output. The inverse of this function is denoted by f^-1(x) takes the output values produced by f(x) and converts them back to the input values.

For example, let’s say f(x) = 2x. It doubles the number which is given as input, its inverse should make them half to g

solving inverse functions

steps to finding inverse