For $0 \leq x \leq 2\pi$, the function $f$ is given by $f(x) = 2 - 3 \cos x$.
(i)[2]
State the range for $f$.
(ii)[2]
Sketch the curve for $y = f(x)$.
(iii)[1]
The function $g$ is given by $g(x) = 2 - 3\cos x$ for $0 \leq x \leq p$, where $p$ is a constant. State the greatest value of $p$ such that $g$ has an inverse.
(iv)[2]
For this value of $p$, determine an expression for $g^{-1}(x)$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Range correctly given as $-1 \le f(x) \le 5$” …