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9709 P11 - Jun 2022 - Q6
741

The function f is defined as follows:

\(f(x) = \frac{x^2 - 4}{x^2 + 4}\) for \(x > 2\).

(a) Find an expression for \(f^{-1}(x)\).

(b) Show that \(1 - \frac{8}{x^2 + 4}\) can be expressed as \(\frac{x^2 - 4}{x^2 + 4}\) and hence state the range of \(f\).

(c) Explain why the composite function \(ff\) cannot be formed.

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