The functions $\mathrm{f}$ and $\mathrm{g}$ are defined as follows: \(\mathrm{f}: x \mapsto \dfr

Question

The functions $\mathrm{f}$ and $\mathrm{g}$ are defined as follows: $\mathrm{f}: x \mapsto \dfrac{5 - x}{1 - x}, x \in \mathbb{R}, x \ne 1$ Explain why $\mathrm{f}$ has an inverse, $\mathrm{f}^{-1}$, and show that $\mathrm{f}^{-1} = \mathrm{f}$. [4] Evaluate $\mathrm{f}^{51}(4)$.[2]

Accepted Answer

(i) f = f⁻¹ (shown), (ii) f⁵(4) = -1/3

2009 HCI P1 Q9

2009 HCI P1 Q9

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