Mathematics 9709 · AS & A Level · Functions

Functions — practice question

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 $-1 \le f(x) \le 5$

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