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

(ii) ${{\mathrm{f}}^{3}}(x)=x,x\in \mathbb{R},x\ne 1,x\ne 0$; ${{\mathrm{f}}^{2020}}\left( x \right)=\frac{1}{1-x},x\in \mathbb{R},x\ne 1,x\ne 0$

N2014 P1 Q1 [Modified]

N2014 P1 Q1 [Modified]

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