KCET · Maths · Functions
Domain of the function \(f\), given by \(f(x)=\frac{1}{\sqrt{(x-2)(x-5)}}\) is
- A \((-\infty, 2] \cup[5, \infty)\)
- B \((-\infty, 2) \cup(5, \infty)\)
- C \((-\infty, 3) \cup[5, \infty)\)
- D \((-\infty, 3] \cup(5, \infty)\)
Answer & Solution
Correct Answer
(B) \((-\infty, 2) \cup(5, \infty)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=\frac{1}{\sqrt{(x-2)(x-5)}} \\ & \Rightarrow(x-2)(x-5)\gt0 \\ & \Rightarrow x \in(-\infty, 2) \cup(5, \infty)\end{aligned}\)
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