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Tim Gan Math

2014 A-Level H2 Mathematics

0 of 8 completed
Question 1Functions7 marks

The function \(\mathrm{f}\) is defined by

\(\mathrm{f}:x\mapsto \frac{1}{1-x}\), \(x\in \mathbb{R}\), \(x\ne 1\), \(x\ne 0\).

  1. Show that \({{\mathrm{f}}^{2}}\left( x \right)={{\mathrm{f}}^{-1}}\left( x \right)\). [4]
  2. Find \({{\mathrm{f}}^{3}}\left( x \right)\) and \({{\mathrm{f}}^{2020}}\left( x \right)\) in simplest form. [3]
Solution step 1, image 1
Solution step 2, image 1

Final Answer:

(i) \(\mathrm f^2(x)=\mathrm f^{-1}(x)=1-\dfrac1x\), for \(x\in\mathbb R\setminus\{0,1\}\) (ii) \(\mathrm f^3(x)=x\) and \(\mathrm f^{2020}(x)=\dfrac{1}{1-x}\), for \(x\in\mathbb R\setminus\{0,1\}\)