The function $\mathrm{g}$ is defined by $\mathrm{g}:x \mapsto \ln(x-\sqrt{3})$, for \(x \in

Question

The function $\mathrm{g}$ is defined by $\mathrm{g}:x \mapsto \ln(x-\sqrt{3})$, for $x \in \mathbb{R},\ x>\sqrt{3}$. Explain how you know $\mathrm{g}^{-1}$ exists.[2] Find $\mathrm{g}^{-1}(x)$ and write down its domain.[3] Solve $\mathrm{g}(x)=0$ exactly.[1] Hence, without using a calculator, solve the inequality $\dfrac{\mathrm{g}(x)}{(x-3)(x+1)} \ge 0$.[3]

Accepted Answer

(b) $\mathrm{g}^{-1}(x)=e^x+\sqrt3$, domain $\mathbb R$ (c) $x=1+\sqrt3$ (d) $\sqrt33$

2025 RI Promo Q8

2025 RI Promo Q8

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