These Ten-Year-Series (TYS) worked solutions with video explanations for 2013 A Level H2 Mathematics Paper 2 Question 1 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2013 A Level H2 Math Paper 2 Question 1
Functions $\text{f}$ and $\text{g}$ are defined by
$\text{f}:x\mapsto \frac{2+x}{1-x}$, $x\in \mathbb{R}$, $x\ne 1$,
$\text{g}:x\mapsto 1-2x$, $x\in \mathbb{R}$.
(i)
Explain why the composite function $\text{fg}$ does not exist.
[2]
(i) Explain why the composite function $\text{fg}$ does not exist.
[2]
(ii)
Find an expression for $\text{gf}\left( x \right)$ and hence, or otherwise, find ${{\left( \text{gf} \right)}^{-1}}\left( 5 \right)$.
[4]
(ii) Find an expression for $\text{gf}\left( x \right)$ and hence, or otherwise, find ${{\left( \text{gf} \right)}^{-1}}\left( 5 \right)$.
[4]
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