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AP EAMCET · Maths · Functions

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

  1. A \(\left[0, \frac{3}{2}\right]\)
  2. B \(\left(0, \frac{3}{2}\right]\)
  3. C \([0,1]\)
  4. D \((0,1]\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left(0, \frac{3}{2}\right]\)

Step-by-step Solution

Detailed explanation

\(\begin{gathered}\text { Since } \log _{10}\left(\frac{3-x}{x}\right) \geq 0 \\ \Rightarrow \frac{3-x}{x} \geq 1 \quad \text { also Since, } \frac{3-x}{x}>0 \\ \Rightarrow x \in\left(0, \frac{3}{2}\right]\end{gathered}\) Hence domain of…