Determine the inverse function: Find the inverse function for .

If we solve for x as a function of y, we will have a candidate for the inverse. We can then re-express it in terms of x and try out the inverse property.

. Thus the inverse function, f ^-1, has the form

. If we let x be the independent variable, we have

as the inverse function. Note that this function is its own inverse!

Now we should test the inverse function by using the definition of the inverse function:

, and we see that the definition is satisfied.