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If (f(x)=\sqrt{x+3}) and (g(x)=\sqrt{x-1}), what are the correct simplified form and domain of ((fg)(x))?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?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\sqrt{x^2+2x-3},\ x\ge1)(\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}).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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