Question

The domain of $f\left(x\right)=\log \left\{\right(x-3\left)\right(6-x\left)\right\}$ is

• A. $(3,\infty )$
• B. $(3,6)$
• C. $(0,\infty )$
• D. $(-\infty ,\infty )$

Answer 1

The correct option is B $(3,6)$

$(x-3)(6-x)>0$
$\Rightarrow$ either both should be +ve or both -ve
$\Rightarrow (x-3)(x-6)<0$
$x\in (3,6).$