Problem #540
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540
A function f is defined by \(f : x \mapsto 3 - 2 \tan\left(\frac{1}{2}x\right)\) for \(0 \leq x < \pi\).
- State the range of \(f\). [1]
- State the exact value of \(f\left(\frac{2}{3}\pi\right)\). [1]
- Sketch the graph of \(y = f(x)\). [2]
- Obtain an expression, in terms of \(x\), for \(f^{-1}(x)\). [3]
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