What is the Inverse of f(x)=x^2-2x

Question

I need to know the steps to understand how to solve.

Answer 1

There is no inverse function, because we would need to map 0 to both 0 and 2 (for example), and a function by definition must have a unique mapping of the domain to the range. A one-to-many mapping is not permissible. f(x) is a parabola so in general there are two different values of x mapping to the same value. The inverse function would need to map that value to two different values, which is not possible.