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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