Question

How do you find the inverse of `f(x)=(x+2)^2-4`?

Answer 1

This function is not one-one, so has no well defined inverse unless you restrict the domain.

Explanation:

Note that `f(-3) = f(-1) = -3`, so `f^(-1)(-3)` is not well defined.

If we restrict the domain of `f(x)` it is possible to construct an inverse.

For example, if the domain of `f(x)` is `[-2, oo)` then

`f^(-1)(y) = sqrt(y+4)-2`