AP EAMCET · Maths · Functions
The domain of the real valued function \(f(x)=\frac{\sqrt{\log _{0.5}(x-3)}}{\sqrt{x-1}}\) is
- A \((3,4]\)
- B \([4, \infty)\)
- C \((1, \infty)\)
- D \((1,3)\)
Answer & Solution
Correct Answer
(A) \((3,4]\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\frac{\sqrt{\log _{0.5}(x-3)}}{\sqrt{x-1}}\) \(\log _{0.5}(x-3) \geq 0\) \(\Rightarrow \quad x-3 \leq(0.5)^0\) \(\Rightarrow \quad x \leq 4\) ...(A) \(x-3>0\) \(x>3\) ...(B) \(x-1>0\) \(x>1\) ...(C) \(A \cap B \cap C \Rightarrow 3 < x \leq 4\) i.e. \(x \in(3,4]\)
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