Moderate -0.8 This is a straightforward composite function question requiring only the definition fg(x) = f(g(x)) = ln(x³) = 3ln(x) using log laws, followed by recognizing a simple vertical stretch transformation. Both parts are routine C3 exercises with minimal steps and no problem-solving required.
3 The functions \(\mathrm { f } ( x )\) and \(\mathrm { g } ( x )\) are defined for the domain \(x > 0\) as follows:
$$\mathrm { f } ( x ) = \ln x , \quad \mathrm {~g} ( x ) = x ^ { 3 } .$$
Express the composite function \(\mathrm { fg } ( x )\) in terms of \(\ln x\).
State the transformation which maps the curve \(y = \mathrm { f } ( x )\) onto the curve \(y = \mathrm { fg } ( x )\).
3 The functions $\mathrm { f } ( x )$ and $\mathrm { g } ( x )$ are defined for the domain $x > 0$ as follows:
$$\mathrm { f } ( x ) = \ln x , \quad \mathrm {~g} ( x ) = x ^ { 3 } .$$
Express the composite function $\mathrm { fg } ( x )$ in terms of $\ln x$.\\
State the transformation which maps the curve $y = \mathrm { f } ( x )$ onto the curve $y = \mathrm { fg } ( x )$.
\hfill \mbox{\textit{OCR MEI C3 2005 Q3 [3]}}