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

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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 $f (- 3) = f (- 1) = - 3$ $f(-3) = f(-1) = -3$ , so $f^{- 1} (- 3)$ $f^(-1)(-3)$ is not well defined.

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

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

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

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