(a)[3]
Find a formula for $f^{-1}(x)$.
(b(i))[1]
State the domain of the inverse function $f^{-1}$.
(b(ii))[1]
State the range of the inverse function $f^{-1}$.
(c)[3]
For $a = \frac{7}{2}$, Solve the equation $gf(x) = 0$.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The functions $f$ and $g$ are given by $f(x) = (x + a)^2 - a$ for $x \leq -a$, and by $g(x) = 2x - 1$ for $x \in \mathbb{R}$, where $a$ is a positive constant.