For $-\frac{1}{2}\pi \leq x \leq \frac{1}{2}\pi$, the function $f$ is specified by $f : x \mapsto 4\sin x - 1$.
(i)[2]
State the set of values of $f$.
(ii)[3]
Find the coordinates of the points where the curve $y = f(x)$ cuts the coordinate axes.
(iii)[2]
Sketch the graph for $y = f(x)$.
(iv)[4]
Obtain a formula for $f^{-1}(x)$, and state both the domain and the range of $f^{-1}$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the function as $f(x)=4\sin x-1$ for $-\frac{\pi}{2}<x<\frac{\pi}{2}$.” …