(i)[3]
Solve $f(x) + 4 = 0$, giving your answer correct to 1 decimal place.
(ii)[5]
Find an expression for $f^{-1}(x)$ together with the domain of $f^{-1}$.
(iii)[3]
On one diagram, sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The function $f$ has rule $f(x) = 3 \tan\left(\frac{1}{2}x\right) - 2$, for $-\frac{1}{2}\pi \leq x \leq \frac{1}{2}\pi$.
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This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rewrites in the form $\tan\left(\frac{x}{2}\right)=-\frac23$” …
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