(a)[4]
Since $g g(2) = 10$ and $f^{-1}(2) = 14$, find the values of $a$ and $b$.
(b)[2]
Using these values of $a$ and $b$, find an expression for $g f(x)$ in the form $cx + d$, where $c$ and $d$ are constants.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The functions $f$ and $g$ are given for $x \in \mathbb{R}$ by $f: x \mapsto \frac{1}{2}x - a$ and $g: x \mapsto 3x + b$, with $a$ and $b$ constant.