The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{-x-3}{x+1}$, for $\mathrm{ }x\in

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{-x-3}{x+1}$, for $\mathrm{ }x\in \mathbb{R}$, $x
e k$ State the value of $k$ and explain why this value has to be excluded from the domain of $\mathrm{f}$. [2] Find ${{\mathrm{f}}^{-1}}$. Hence find ${{\mathrm{f}}^{2}}\left( x ight)$. [3] The function $\mathrm{g}$ is defined by $\mathrm{g}:x\mapsto \sqrt{x+1}$, $x\in \mathbb{R}$, $x>-1$ Find the range of $\mathrm{fg}$. [2]

Accepted Answer

(i) $k=-1$ (ii) ${{\mathrm{f}}^{2}}\left( x \right)=x$ (iii) ${{\mathrm{R}}_{\mathrm{fg}}}=\left( -3,-1 \right)$

2023 SAJC Promo Q8

2023 SAJC Promo Q8

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