Inverse function Q

Quote:

Originally Posted by NeedHelp18

How to find inverse of function with restricted domain?

g(x)= x^2 - 4x ; x >= 2

$y = x^2 - 4x$

swap variables ...

$x = y^2 - 4y$

complete the square and solve for y ...

$x + 4 = y^2 - 4y + 4$

$x + 4 = (y - 2)^2$

$\pm \sqrt{x + 4} = y - 2$

$y = \pm \sqrt{x + 4} + 2$

since $x \geq 2$ in the original function, $y \geq 2$ for the inverse

$g^{-1}(x) = \sqrt{x + 4} + 2$