These Ten-Year-Series (TYS) worked solutions with video explanations for 2015 A Level H2 Mathematics Paper 2 Question 3 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2015 A Level H2 Math Paper 2 Question 3
(a)
The function $\text{f}$ is defined by $\text{f}:x\mapsto \frac{1}{1-{{x}^{2}}}$, $x\in \mathbb{R}$, $x>1$.
(a) The function $\text{f}$ is defined by $\text{f}:x\mapsto \frac{1}{1-{{x}^{2}}}$, $x\in \mathbb{R}$, $x>1$.
(i) Show that $\text{f}$ has an inverse.
[2]
(i) Show that $\text{f}$ has an inverse.
[2]
(ii) Find ${{\text{f}}^{-1}}\left( x \right)$ and state the domain of ${{\text{f}}^{-1}}$.
[3]
(ii) Find ${{\text{f}}^{-1}}\left( x \right)$ and state the domain of ${{\text{f}}^{-1}}$.
[3]
(b)
The function $\text{g}$ is defined by $\text{g}:x\mapsto \frac{2+x}{1-{{x}^{2}}}$, $x\in \mathbb{R}$, $x\ne \pm 1$. Find algebraically the range of $\text{g}$, giving your answer in terms of $\sqrt{3}$ as simply as possible.
[5]
(b) The function $\text{g}$ is defined by $\text{g}:x\mapsto \frac{2+x}{1-{{x}^{2}}}$, $x\in \mathbb{R}$, $x\ne \pm 1$. Find algebraically the range of $\text{g}$, giving your answer in terms of $\sqrt{3}$ as simply as possible.
[5]
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