(a)[1]
State the range for $f$.
(b)[2]
Find the inverse function $f^{-1}(x)$.
(c)[3]
With $a = -\frac{5}{3}$, solve $f(x) = g(x)$.
(d)[5]
If $g\,f^{-1}(12) = 62$ instead, find the possible values of $a$.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The functions $f$ and $g$ are given by:
$f(x) = (x - 2)^2 - 4$ for $x \geq 2$,
$g(x) = ax + 2$ for $x \in \mathbb{R}$,
with $a$ as a constant.