What is the inverse of a function and how do you find it?

A function, f(x), is something that takes various input values of x, and for each one, generates an output value, e.g. if f(x) = x² then when x=3, f(x) = f(3) = (3)² = 9, which is the output of the function. - The inverse of a function, f^-1(x), essentially undoes the work of the function, e.g. if f(x) = x² then f^-1(x) = x^1/2 , so it can be thought of as the exact opposite of the original function. Finding the inverse of a function can be done in 4 simple steps - as an example, say we have a function f(x) = 2x+1: Step 1. To make everything easier to write, we first rename f(x) as y, by writing y = f(x), e.g. write y = 2x+1. Step 2. Now swap the x's and y's, e.g. x = 2y+1, this is what 'inverts' the function. Step 3. Rearrange the equation to make y the subject, e.g. x = 2y+1 then x-1 = 2y then y = (x-1)/2. Step 4. We now have our inverse function, this being whatever y equals, so it can be written as f^-1(x) = (x-1)/2.