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Question Number 68546 by aliesam last updated on 13/Sep/19

$$findtherangeanddomainoff\left(x\right)$$$$$$$$f\left(x\right)=\sqrt{{sin}^{-1}\left(ln\frac{x}{10}\right)}$$

Answered by MJS last updated on 13/Sep/19

$$\sqrt{u}\in \mathbb{R}\Rightarrow u⩾0$$$$\arcsin v\in \mathbb{R}\Rightarrow -1⩽v⩽1$$$$\sqrt{\arcsin v}\in \mathbb{R}\Rightarrow 0⩽v⩽1$$$$0⩽\ln \frac{x}{10}⩽1\Rightarrow 10⩽x⩽10\mathrm{e}$$$$\mathrm{domain}:10⩽x⩽10\mathrm{e}$$$$\mathrm{range}:0⩽y⩽\frac{\pi }{\sqrt{2}}$$

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