How to find inverse of function with restricted domain?
g(x)= x^2 - 4x ; x >= 2
$\displaystyle y = x^2 - 4x$
swap variables ...
$\displaystyle x = y^2 - 4y$
complete the square and solve for y ...
$\displaystyle x + 4 = y^2 - 4y + 4$
$\displaystyle x + 4 = (y - 2)^2$
$\displaystyle \pm \sqrt{x + 4} = y - 2$
$\displaystyle y = \pm \sqrt{x + 4} + 2$
since $\displaystyle x \geq 2$ in the original function, $\displaystyle y \geq 2$ for the inverse
$\displaystyle g^{-1}(x) = \sqrt{x + 4} + 2$