Question

Find the inverse of the function f(x) = (x - 4) 2 - 5 if x ≥ 4.

Answer 1

Same here, we do a quick switcharoo on the variables first,

$\bf \stackrel{f(x)}{y}=(x-4)^2-5\qquad inverse\implies \boxed{x}=\left( \boxed{y}-4 \right)^2-5 \\\\\\ x+5=(y-4)^2\implies \pm\sqrt{x+5}=y-4\implies \pm\sqrt{x+5}+4=y$