Finding an Inverse

An **inverse function **is a function that undoes another function, much like addition undoes subtraction. Inverse functions use inverse operations to turn inputs into outputs and vice versa.

The function,* f ^{-1} (x)*, is defined as the inverse function of

There are a couple of ways to think about the inverse of a function. Inverses can be approached by looking at graphs or performing algebraic operations. In either case, it comes down to the basic notion that the inverse of a function reverses the x and y coordinates. In other words, for every ordered pair *(x, y)* in a function there will be an ordered pair *(y, x) *in the inverse function.

The graph of an inverse of a function is reflected over the line *y = x. *Reflecting over the line *y = x* produces the goal of reversing the x and y coordinates.

In the graph below, the original function __ __is reflected over the line y =x and gives us the inverse function .