It seems as though there exists an inverse function for every function there is. Some people say the inverse function of a non-injective is useless, but you could set f(a) equal to f(b), and find all the instances when f(a) equals f(b), and use that to figure out all the possible x values for a particular y value. For example, the inverse function of x^2 is sqrt(x). If you set f(a) equal to f(b), you find that a can be equal to either b or -b, and vice-versa. Tell me if I'm wrong.