2022 ASRJC P1 Q8

Timothy Gan

2022 ASRJC P1 Q8

(a)

Functions $\text{f}$ and $\text{g}$ are defined by

$\text{f}:x\to {{x}^{2}}$, $x<0$.
$\text{g}:x\to \frac{1}{x}$, $x>0$.

(i) Explain why the composite function $\text{gf}$ exists.

[1]

(ii) Find the exact value of ${{\text{f}}^{-1}}{{\text{g}}^{-1}}\left( 3 \right)$. Show your workings clearly.

[3]

(b)

For real values $a$, the function $h$ is defined by

$\text{h}:x\mapsto ax-\frac{1}{x}$, $x<0$.

(i) If $a$ is negative, explain clearly with a well-labelled diagram, why ${{\text{h}}^{-1}}$ does not exist.

[4]

(ii) If $a=1$, find ${{\text{h}}^{-1}}$ in similar form.

[3]

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Published: 7th September 2023

Written by

Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.

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