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  4. Domain of y=√ log 10 (3 x-x2/2) is

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

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Solution:

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