Moderate -0.8 This question requires computing two function compositions and solving a linear equation, but all steps are straightforward applications of function notation. Finding ff(x) = f(f(x)) and gf(2) = g(f(2)) involves direct substitution with no conceptual challenges, making it easier than average for A-level.
1 Functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 10 - 3 x , \quad x \in \mathbb { R } , \\
& \mathrm {~g} : x \mapsto \frac { 10 } { 3 - 2 x } , \quad x \in \mathbb { R } , x \neq \frac { 3 } { 2 }
\end{aligned}$$
Solve the equation \(\mathrm { ff } ( x ) = \mathrm { gf } ( 2 )\).
1 Functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 10 - 3 x , \quad x \in \mathbb { R } , \\
& \mathrm {~g} : x \mapsto \frac { 10 } { 3 - 2 x } , \quad x \in \mathbb { R } , x \neq \frac { 3 } { 2 }
\end{aligned}$$
Solve the equation $\mathrm { ff } ( x ) = \mathrm { gf } ( 2 )$.
\hfill \mbox{\textit{CAIE P1 2016 Q1 [3]}}