| Exam Board | CAIE |
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| Module | P1 (Pure Mathematics 1) |
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| Year | 2015 |
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| Session | November |
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| Topic | Composite & Inverse Functions |
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1 Functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 3 x + 2 , \quad x \in \mathbb { R } ,
& \mathrm {~g} : x \mapsto 4 x - 12 , \quad x \in \mathbb { R } .
\end{aligned}$$
Solve the equation \(\mathrm { f } ^ { - 1 } ( x ) = \operatorname { gf } ( x )\).