Moderate -0.8 This is a straightforward P1 question requiring students to find the inverse of f, set it equal to g(x), and solve a linear equation. It involves only basic algebraic manipulation with no conceptual challenges beyond recalling the inverse function procedure.
2 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 \(\mathrm { f } ^ { - 1 } ( x ) = \mathrm { gf } ( x )\).
2 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 $\mathrm { f } ^ { - 1 } ( x ) = \mathrm { gf } ( x )$.\\
\hfill \mbox{\textit{CAIE P1 2020 Q2 [4]}}