Q52 / 155 · WBJEE 2022 · Mathematics

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

  • A
    $x < 1$
  • B
    $2 < x$
  • Correct answer
    C
    $1 \leq x \leq 2$
  • D
    $2 < x < 3$

Solution

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

Hence, the correct answer is option: 'C'.

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