Functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto \frac{2+x}{1-x}$, $x\in

Question

Functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto \frac{2+x}{1-x}$, $x\in \mathbb{R}$, $x
e 1$, $\mathrm{g}:x\mapsto 1-2x$, $x\in \mathbb{R}$. Explain why the composite function $\mathrm{fg}$ does not exist. [2] Find an expression for $\mathrm{gf}\left( x ight)$ and hence, or otherwise, find ${{\left( \mathrm{gf} ight)}^{-1}}\left( 5 ight)$. [4]

Accepted Answer

(ii) $\mathrm{gf}\left( x \right) = \frac{3x+3}{x-1},\ x \in \mathbb{R},\ x e 1,\ \left(\mathrm{gf}\right)^{-1}\left( 5 \right) = 4$

N2013 P2 Q1

N2013 P2 Q1

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