4400 Higher June 2004 Paper 3 Q19

EdexcelHigherOld spec6 marksFunctions

19

\[\mathrm{f} : x \mapsto 2x - 1\] \[\mathrm{g} : x \mapsto \frac{3}{x},\ x \neq 0\]
(a) Find the value of
(i) \(\mathrm{f}(3)\),
(ii) \(\mathrm{fg}(6)\). (2)
(b) Express the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1} : x \mapsto\) ... (2)
(c)
(i) Express the composite function \(\mathrm{gf}\) in the form \(\mathrm{gf} : x \mapsto\) ...
(ii) Which value of \(x\) must be excluded from the domain of \(\mathrm{gf}\)? (2)
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