Problem

Functions $f$ and $g$ are defined by

$f(x)=(x+3)^2-12\quad\text{for }x\geq 0,$

$g(x)=2x-5\quad\text{for }x\in\mathbb{R}.$

(a) State the range of $f$.

(b) Find an expression for $f^{-1}(x)$.

(c) Solve the equation $gf(x)=69$.