The curve $y=\ln(x^2)$, where $x0$, undergoes, in succession, the following transformat

Question

The curve $y=\ln(x^2)$, where $x>0$, undergoes, in succession, the following transformations to obtain the curve $y=\mathrm{f}(x)$: $A$: A scaling parallel to the $x$-axis with scale factor $2$, $B$: A translation by $\ln 9$ units in the positive $y$-direction. Find the equation of the curve $y=\mathrm{f}(x)$, showing your workings clearly.[2] It is given that the curve $y=\mathrm{f}(x)$ can be obtained from the curve $y=\ln(x^2)$ by a single transformation. Describe this transformation.[1]

Accepted Answer

(a) $y=2\ln\left(\dfrac{3x}{2}\right),\ x>0$ (b) Scaling parallel to the $x$-axis with scale factor $\dfrac{2}{3}$.

2026 HCI Promo Q1

2026 HCI Promo Q1

Solution:

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