Question

Domain of the function
$y=\sqrt{(x^2-3x-10){\log }^2(x-3)}$ is

• A. $[5,+\infty )$
• B. $4[5,+\infty )$
• C. $[0,+\infty )$
• D. $none$

Answer 1

The correct option is A $[5,+\infty )$

The value of (x-3) should be greater than 0 since it is operated by log,

$\therefore$ $x\in$ $(3,\infty )$ -(i)

$(x^2-3x-10)lo{g}^2(x-3)\ge$ 0 (Since, any value under root is either greater than or equal to 0)

$\Rightarrow$ $x^2-3x-10\ge$ 0 (Since $log^2(x -3) will always be positive or 0)

$\Rightarrow$$x\in$ $(-\infty ,-2]\cup [5,\infty )$ -(ii)

Taking intersection of (i) and (ii),

Domain of the function is $[5,\infty )$

So, the correct option is 'A'.