(i)[2]
Solve $gf(x) = 1$, and give your answer in terms of $\pi$.
(ii)[4]
Solve $fg(x) = 1$, and give your answers correct to $2$ decimal places.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
For $-\tfrac{1}{2}\pi \leq x \leq \tfrac{1}{2}\pi$, the functions $f$ and $g$ are given by $f(x) = \tfrac{1}{2}x + \tfrac{1}{6}\pi$ and $g(x) = \cos x$.
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Forms the equation $\cos\left(\frac{x}{2} + \frac{\pi}{6}\right) = 1$ correctly” …
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