Question

find the inverse of the function y=x^2-12

Answer 1

Swap the y with the x. So
$y=x^2-12$
$x = y^2-12$
Now solve for y
$x = y^2-12$
$x + 12 = y^2$
$\sqrt{x + 12} = \sqrt{y^2}$
$\sqrt{x + 12} = y$
$y = \sqrt{x + 12}$
Inverse notation:
$f(x)^{-1} = \sqrt{x + 12}$