The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{x+2}{x-1}$, for $x\in \mathbb{R}$

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{x+2}{x-1}$, for $x\in \mathbb{R}$, $x
e 1$. Find ${{\mathrm{f}}^{2}}(x)$ and ${{\mathrm{f}}^{2012}}(x)$. [3] The function $\mathrm{g}$ is defined by $\mathrm{g}:x\mapsto \cos x$, for $0 Explain why the composite function $\mathrm{fg}$ exists. [2] Define $\mathrm{fg}$, giving its domain. [2] Find the range of $\mathrm{fg}$. [1]

Accepted Answer

(i) ${{\mathrm{f}}^{2}}(x)=x,\quad {{\mathrm{f}}^{2012}}(x)=x$(ii) Since ${{R}_{\mathrm{g}}}\subseteq {{D}_{\mathrm{f}}}$, $\mathrm{fg}$ exists. (iii) $\mathrm{fg}:x\mapsto \frac{\cos x+2}{\cos x-1},\quad 0<x<2\pi $ (iv) ${{R}_{\mathrm{fg}}}=\left( -\infty ,-\frac{1}{2} \right]$

2012 JJC Promo Q5

2012 JJC Promo Q5

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