We can view a function as something that maps things of one type to things of another type. The inverse of a function tells you how to get back to the original value. We do this a lot in everyday life, without really thinking about it.

For example, think of a sports team. Each player has a name and a number. So if you knew a players name and wanted to know their number, you could think of this as a function from players to their numbers. Now, if you wanted to do the reverse, find a players name given their number, you would be using the inverse of this function.

Another example: suppose I am travelling at 60 miles per hour, and want to know how far I have gone in x hours. Then this could be represented by the function`f(x) = 60 * x`

Now I want to know the inverse: If I know I have travelled x miles how long have I been travelling for? `f^{-1}(x) = x/60`

Suppose there is a legal limit to the angle an entrance ramp can be. If I have the horizontal length of a ramp and the vertical height I can compute the angle by using the inverse tangent to find the angle of the ramp. I can also use the square root (which is the inverse function of the square) to find the length of the ramp using `c = sqrt(a^2+b^2)`