The functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto 2-{{\left( x-2 \righ

Question

The functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto 2-{{\left( x-2 ight)}^{2}}$ for $x\le 0$, $x\in \mathbb{R}$, and $\mathrm{g}:x\mapsto \left\{ \begin{matrix} 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,\,\,x\ge 3,\,x\in \mathbb{R} \ x+1\,\,\,\,\,\,\,\mathrm{for}\,\,\,x<3,x\in \mathbb{R} \ \end{matrix} ight.$ Define ${{\mathrm{f}}^{-1}}$ in a similar form. [3] Explain why $\mathrm{g}$ does not have an inverse. [2] Find the range of values of $\alpha $ such that $\mathrm{fg}\left( \alpha ight)$ exists. [2]

Accepted Answer

(i) $\mathrm f^{-1}:x\mapsto2-\sqrt{2-x}$, $x\leq-2$ (ii) $\mathrm g$ is not one-to-one (iii) $\alpha\leq-1$

2021 TJC P2 Q1

2021 TJC P2 Q1

Video Solution:

Solution:

Solution locked