Q63 / 180 · KCET 2025 · Mathematics

Domain of the function $f$, given by $f(x)=\frac{1}{\sqrt{(x-2)(x-5)}}$ is

A
$(-\infty, 2] \cup[5, \infty)$
Correct answer
B
$(-\infty, 2) \cup(5, \infty)$
C
$(-\infty, 3) \cup[5, \infty)$
D
$(-\infty, 3] \cup(5, \infty)$

Solution

$\begin{aligned} & f(x)=\frac{1}{\sqrt{(x-2)(x-5)}} \\ & \Rightarrow(x-2)(x-5)\gt0 \\ & \Rightarrow x \in(-\infty, 2) \cup(5, \infty)\end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions