N2007 P1 Q2
N2007 P1 Q2
Junior College 2
6 marks
Functions \(f\) and \(g\) are defined by \(f:x\mapsto\frac1{x-3}\) for \(x\in\mathbb R,x\ne3\), and \(g:x\mapsto x^2\) for \(x\in\mathbb R\).
- Only one of the composite functions fg and gf exists. Give a definition (including the domain) of the composite that exists, and explain why the other composite does not exist.[3]
- Find \(f^{-1}(x)\) and state the domain of \(f^{-1}\).[3]
Solution:
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Answer:(i) \(gf(x)=1/(x-3)^2,x\ne3\). (ii) \(f^{-1}(x)=3+1/x,x\ne0\).
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