Inverse functions are functions that 'undo' another function. Given a function f(x), the inverse function f^(-1) satisfies f(f^(-1)(x)) = x and f^(-1)(f(x)) = x. In other words, the inverse function 'un-does' what the original function does.

For example, if we have a function f(x) = 2x, then the inverse function f^(-1)(x) = x/2. This means that if we input x = 4 into f(x), we get output 8, and if we input x = 8 into f^(-1)(x), we get output 4.

Inverses are useful in many real-world applications, such as finding the cost of an item on sale or solving equations involving fractions. They also play a key role in calculus, where they are used to find derivatives and integrals.

Math is Fun!: Try graphing f(x) = 2x and f^(-1)(x) = x/2 on Desmos and explore their relationships!