Moderate -0.8 This question requires finding the inverse of a linear function and composing two linear functions, then solving a linear equation. All steps are routine algebraic manipulations with no conceptual challenges—standard P1 material requiring only direct application of well-practiced techniques.
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 \(\mathrm { f } ^ { - 1 } ( x ) = \operatorname { gf } ( x )\).
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 $\mathrm { f } ^ { - 1 } ( x ) = \operatorname { gf } ( x )$.
\hfill \mbox{\textit{CAIE P1 2015 Q1 [4]}}