Question

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

• A. $x<1$
• B. $2<x$
• C. $1\le x\le 2$
• D. $2<x<3$

Answer 1

Answer: (C)

Hint: ${\log }_{10}\left(\frac{3x-x^2}{2}\right)\ge 0$
Or ${\log }_{10}\left(\frac{3x-x^2}{2}\right)\ge {\log }_{10}1$
or $x^2-3x+2\le 0$
or $x\in [1,2]$ and $\frac{3x-x^2}{2}>0$
$\Rightarrow x\in [1,2]$