N2014 P1 Q1
N2014 P1 Q1
Junior College 2
5 marks
The function \(f\) is defined by \[f:x\mapsto\frac1{1-x},\quad x\in\mathbb R,\quad x\ne1,\quad x\ne0.\]
- Show that \(f^2(x)=f^{-1}(x)\).[4]
- Find \(f^3(x)\), giving your answer in its simplest form.[1]
Solution:
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Answer:(i) \(f^2(x)=f^{-1}(x)=\frac{x-1}{x}\) (shown). (ii) \(f^3(x)=x\).
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