For $0 \leq x \leq 2\pi$, the function $f$ is defined by $f : x \mapsto 3\cos x - 2$.
(i)[3]
Solve the equation $f(x) = 0$ for $x$.
(ii)[2]
State the range of $f$.
(iii)[2]
Sketch $y = f(x)$.
(iv)[1]
For $0 \leq x \leq k$, the function $g$ is defined by $g : x \mapsto 3\cos x - 2$. State the maximum value of $k$ for which $g$ has an inverse.
(v)[2]
Determine an expression for $g^{-1}(x)$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Solving $3\cos x-2=0$” …
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