The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{1}{1-x}$, $x\in \mathbb{R}$

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{1}{1-x}$, $x\in \mathbb{R}$, $x\ne 1$, $x\ne 0$. Show that ${{\mathrm{f}}^{2}}\left( x \right)={{\mathrm{f}}^{-1}}\left( x \right)$. [4] Find ${{\mathrm{f}}^{3}}\left( x \right)$ and ${{\mathrm{f}}^{2020}}\left( x \right)$ in simplest form. [3]

Accepted Answer

(i) $\mathrm f^2(x)=\mathrm f^{-1}(x)=1-\dfrac1x$, for $x\in\mathbb R\setminus\{0,1\}$ (ii) $\mathrm f^3(x)=x$ and $\mathrm f^{2020}(x)=\dfrac{1}{1-x}$, for $x\in\mathbb R\setminus\{0,1\}$

N2014 P1 Q1 [Modified]

N2014 P1 Q1 [Modified]

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