6 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 \(y = \mathrm { fg } ( x )\).

## Question 6:

| $fg(x) = \ln(x^3) = 3\ln x$ | M1, A1 | $\ln(x^3) = 3\ln x$ |
|---|---|---|
| Stretch scale factor 3 in $y$ direction | B1 | |

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6 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  Q6 [3]}}