Diketahui:
\(g(x) = x + 1\)
\((f \circ g) (x) = 3x + 7\)
Tentukan \(f(x)\)
Cara pemisalan
\begin{equation*}
\begin{split}
(f \circ g) (x) & = 3x + 7 \\\\
f(g(x)) & = 3x + 7 \\\\
f({\color {blue} x + 1}) & = 3x + 7
\end{split}
\end{equation*}
Misalkan:
\begin{equation*}
\begin{split}
{\color {blue} x + 1} & = {\color {blue} m} \\\\
{\color {red} x} & = {\color {red} m - 1}
\end{split}
\end{equation*}
Maka:
\begin{equation*}
\begin{split}
f({\color {blue} x + 1}) & = 3 {\color {red} x} + 7 \\\\
f({\color {blue} m}) & = 3({\color {red} m - 1}) + 7 \\\\
f(m) & = 3m - 3 + 7 \\\\
f(m) & = 3m + 4 \\\\
f(x) & = 3x + 4
\end{split}
\end{equation*}
Cara langsung
\begin{equation*}
\begin{split}
(f \circ g) (x) & = 3x + 7 \\\\
f(g(x)) & = 3x + 7 \\\\
f({\color {red} x + 1}) & = 3x + 7 \\\\
f({\color {red} x + 1}) & = 3({\color {red} x + 1}) + 4 \\\\
f(x) & = 3x + 4
\end{split}
\end{equation*}