find the inverse of the function f(x)=x^2 - 3x
Well, you can find an inverse for (say) x>0. The way to find inverses is rather limited: equate y=f(x) and solve for x. That is the inverse function x=g(y).
Here, we have y=f(x)=x^2-3x or x^2-3x-y=0. Solve this (quadratic for x), and you have obtained the inverse function.