The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{{{x}^{2}}+4}{x}$ , \(x\in \ma

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{{{x}^{2}}+4}{x}$ , $x\in \mathbb{R}$. Give a reason why $\mathrm{f}$ does not have an inverse.[1] The domain is now restricted to $0 < x\le 2$. Find ${{\mathrm{f}}^{-1}}\left( x \right)$ and state its domain, showing your working clearly.[4]

Accepted Answer

(a) $\mathrm f(1)=\mathrm f(4)=5$, so $\mathrm f$ is not one-to-one and has no inverse (b) $\mathrm f^{-1}(x)=\dfrac{x-\sqrt{x^2-16}}{2}$, with domain $[4,\infty)$

2022 DHS Promo Q3

2022 DHS Promo Q3

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