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Question Number 169667 by MathsFan last updated on 05/May/22

$$\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{t}\mathit{h}\mathit{e}\mathit{d}\mathit{o}\mathit{m}\mathit{a}\mathit{i}\mathit{n}\mathit{o}\mathit{f}$$$$\left(\mathit{i}\right)\frac{\mathit{x}}{\sqrt{\mathit{x}+5}}$$$$\left(\mathit{i}\mathit{i}\right)\sqrt{\mathit{x}}+2$$$$\left(\mathit{i}\mathit{i}\mathit{i}\right)\frac{3}{\sqrt{\mathit{x}+2}+5}$$

Answered by FelipeLz last updated on 06/May/22

$$\left(i\right)f\left(x\right)=\frac{x}{\sqrt{x+5}}$$$$\sqrt{x+5}>0\therefore x>-5$$$$D=\{x\in \mathbb{R}\mid x>-5\}=(-5,\mathrm{\infty })$$$$$$$$\left(ii\right)f\left(x\right)=\sqrt{x}+2$$$$\sqrt{x}⩾0\therefore x⩾0$$$$D=\{x\in \mathbb{R}\mid x⩾0\}=[0,\mathrm{\infty })$$$$$$$$\left(iii\right)f\left(x\right)=\frac{3}{\sqrt{x+2}+5}$$$$\sqrt{x+2}⩾0\therefore x⩾-2$$$$D=\{x\in \mathbb{R}\mid x⩾-2\}=[-2,\mathrm{\infty })$$

Commented by MathsFan last updated on 06/May/22

$$thankyousir$$

Commented by peter frank last updated on 06/May/22

$$\mathrm{good}$$

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