*These Ten-Year-Series (TYS) worked solutions with video explanations for 2014 A Level H2 Mathematics Paper 1 Question 1 [Modified] are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.*

**2014 A Level H2 Math Paper 1 Question 1 [Modified]**

The function $\text{f}$ is defined by

$\text{f}:x\mapsto \frac{1}{1-x},x\in \mathbb{R},x\ne 1,x\ne 0$ .

(i)

Show that ${{\text{f}}^{2}}\left( x \right)={{\text{f}}^{-1}}\left( x \right)$.

[4]

(i) Show that ${{\text{f}}^{2}}\left( x \right)={{\text{f}}^{-1}}\left( x \right)$.

[4]

(ii)

Find ${{\text{f}}^{3}}\left( x \right)$ and ${{\text{f}}^{2020}}\left( x \right)$ in simplified forms.

[3]

(ii) Find ${{\text{f}}^{3}}\left( x \right)$ and ${{\text{f}}^{2020}}\left( x \right)$ in simplified forms.

[3]

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