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WBJEE · Maths · Functions

Domain of \(y=\sqrt{\log _{10} \frac{3 x-x^2}{2}}\) is

  1. A \(x < 1\)
  2. B \(2 < x\)
  3. C \(1 \leq x \leq 2\)
  4. D \(2 < x < 3\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(1 \leq x \leq 2\)

Step-by-step Solution

Detailed explanation

\[ \log _{10}\left(\frac{3 x-x^2}{2}\right) \geq 0 \] or \(\log _{10}\left(\frac{3 x-x^2}{2}\right) \geq \log _{10} 1\) or \(x^2-3 x+2 \leq 0\) or \(x \in[1,2]\) and \(\frac{3 x-x^2}{2}>0\) \[ \Rightarrow \mathrm{X} \in[1,2] \]