| Exam Board | CAIE |
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| Module | P1 (Pure Mathematics 1) |
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| Year | 2010 |
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| Session | November |
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| Topic | Composite & Inverse Functions |
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3 Functions f and g are defined for \(x \in \mathbb { R }\) by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 2 x + 3
& \mathrm {~g} : x \mapsto x ^ { 2 } - 2 x
\end{aligned}$$
Express \(\operatorname { gf } ( x )\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants.