Question

The domain of $\frac{1}{\sqrt{x-x^2}}+\sqrt{3x-1-2x^2}$ is

• A. $(\frac{1}{2},11)$
• B. $(\frac{1}{2},31)$
• C. $(\frac{1}{2},17)$
• D. $(\frac{1}{2},41)$

Answer 1

The correct option is A $(\frac{1}{2},11)$

$+\left(x\right)=\frac{1}{\sqrt{x(1-x)}}+\sqrt{3x-1-2x^2}$

Domain of $f\left(x\right)$ : -

$x(1-x)>0$ and $3x-1-2x^2\ge 0$

$2x^2-3x+1\le 0$

$2x(x-1)-1(x-1)\le 0$

$(2x-1)(x-1)\le 0$

Thus taking the intersection of above $2$.

$x\leftarrow [\frac{1}{2},1)$.