The function $\mathrm{f}$ is defined by $\mathrm{f}:x o {{\left( \frac{3}{x-2} ight)}^{2}}$, $x\i

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}:x	o {{\left( \frac{3}{x-2} ight)}^{2}}$, $x\in \mathbb{R}$, $x>2$. Show that ${{\mathrm{f}}^{-1}}$ exists and define it in similar form. [5] Using a new set of axes, sketch the graphs of $\mathrm{f}$, ${{\mathrm{f}}^{-1}}$ and ${{\mathrm{f}}^{-1}}\mathrm{f}$ on the same diagram. [3]

Accepted Answer

$f^{-1}: x \mapsto 2 + \dfrac{3}{\sqrt{x}}$, $x > 0$; $D_{f^{-1}f} = (2, \infty)$, $D_{ff^{-1}} = (0, \infty)$

2022 CJC J1 MYE Q7

2022 CJC J1 MYE Q7

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