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

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Answer 1 · 2016-01-19T19:13:59

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

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

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

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