For $x \in \mathbb{R}$ if $f(x)=\sqrt{\log _{10}\left(\frac{3-x}{x}\right)}$, then the domain of $\mathrm{f}$ is

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Aicharya · Accepted Answer

$\begin{gathered}	ext { Since } \log _{10}\left(\frac{3-x}{x}ight) \geq 0 \ \Rightarrow \frac{3-x}{x} \geq 1 \quad 	ext { also Since, } \frac{3-x}{x}>0 \ \Rightarrow x \in\left(0, \frac{3}{2}ight]\end{gathered}$ Hence domain of $ \begin{aligned} f(x) & =\left(0 \frac{3}{2}ight] \cap(0,3) \ & =\left(0, \frac{3}{2}ight] \end{aligned} $

For $x \in \mathbb{R}$ if $f(x)=\sqrt{\log _{10}\left(\frac{3-x}{x}\right)}$, then the domain of…

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