यदि (f(x)=\sqrt{x+3}) और (g(x)=\sqrt{x-1}) हैं, तो ((fg)(x)) का सही सरलीकृत रूप और प्रांत कौन सा है?
If (f(x)=\sqrt{x+3}) and (g(x)=\sqrt{x-1}), what are the correct simplified form and domain of ((fg)(x))?
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{x^2+2x-3},\ x\ge1\)
Concept
For both square roots, \(x+3\ge0\) and \(x-1\ge0\), so \(x\ge1\). The product is (\sqrt{(x+3)(x-1)}=\sqrt{x-2+2x-3}).
Why this answer is correct
The correct answer is A. \(\sqrt{x^2+2x-3},\ x\ge1\). For both square roots, \(x+3\ge0\) and \(x-1\ge0\), so \(x\ge1\). The product is (\sqrt{(x+3)(x-1)}=\sqrt{x-2+2x-3}).
Exam Tip
दोनों वर्गमूलों के लिए \(x+3\ge0\) और \(x-1\ge0\), इसलिए \(x\ge1\)। गुणनफल (\sqrt{(x+3)(x-1)}=\sqrt{x-2+2x-3}) है।
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