यदि (f(x)=\sqrt{16-x-2}) और (g(x)=\frac{1}{x-1}) हैं, तो ((fg)(x)) का प्रांत क्या है?
If (f(x)=\sqrt{16-x-2}) and (g(x)=\frac{1}{x-1}), what is the domain of ((fg)(x))?
Explanation opens after your attempt
Correct Answer
A. \([-4,4]\setminus{1}\)
Concept
The square root needs \(16-x^2\ge 0\), meaning \(-4\le x\le 4\), and the denominator needs \(x\ne 1\). The domain is the intersection of these conditions.
Why this answer is correct
The correct answer is A. \([-4,4]\setminus{1}\). The square root needs \(16-x^2\ge 0\), meaning \(-4\le x\le 4\), and the denominator needs \(x\ne 1\). The domain is the intersection of these conditions.
Exam Tip
वर्गमूल के लिए \(16-x^2\ge 0\), यानी \(-4\le x\le 4\), और हर के लिए \(x\ne 1\) चाहिए। प्रांत इन शर्तों का प्रतिच्छेद है।
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