यदि (f(x)=\sqrt{x-1}) और (g(x)=\sqrt{5-x}) हों, तो ((f+g)(x)) का domain क्या है?
If (f(x)=\sqrt{x-1}) and (g(x)=\sqrt{5-x}), what is the domain of ((f+g)(x))?
Explanation opens after your attempt
Correct Answer
A. ([1,5])
Concept
Both square roots must be defined, so \(x-1\geq 0\) and \(5-x\geq 0\), giving \(x\in[1,5]\). For a sum, take the intersection of domains.
Why this answer is correct
The correct answer is A. ([1,5]). Both square roots must be defined, so \(x-1\geq 0\) and \(5-x\geq 0\), giving \(x\in[1,5]\). For a sum, take the intersection of domains.
Exam Tip
दोनों square roots defined होने चाहिए, इसलिए \(x-1\geq 0\) और \(5-x\geq 0\), जिससे \(x\in[1,5]\)। sum के लिए domains का intersection लें।
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