Functions $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{ax-1}{x-a},$ \(x\in \mathbb{R},x

Question

Functions $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{ax-1}{x-a},$ $x\in \mathbb{R},x\ne a$, Find ${{\mathrm{f}}^{-1}}$ in a similar form.[3] Hence find the value of ${{\mathrm{f}}^{2015}}\left( 5 \right)$ in terms of $a$, where $a\ne 5$.[2]

Accepted Answer

(i) $f^{-1}:x\mapsto\dfrac{ax-1}{x-a}$, $x\in\mathbb R$, $x\ne a$, requiring $a\ne\pm1$ (ii) $f^{2015}(5)=\dfrac{5a-1}{5-a}$

2011 HCI C2 BT2 Q5

2011 HCI C2 BT2 Q5

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