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If \(f(x)=\sqrt{2x-1}\) and \(g(x)=\sqrt{7-3x}\), what is the domain of ((fg)(x))?यदि \(f(x)=\sqrt{2x-1}\) और \(g(x)=\sqrt{7-3x}\) हैं, तो ((fg)(x)) का प्रांत क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\left[\frac{1}{2},\frac{7}{3}\right]\)\(\left[\frac{1}{2},\frac{7}{3}\right]\)
Both square roots require \(2x-1\ge 0\) and \(7-3x\ge 0\). Hence the domain is \(\left[\frac{1}{2},\frac{7}{3}\right]\).दोनों वर्गमूलों के लिए \(2x-1\ge 0\) और \(7-3x\ge 0\) चाहिए। इसलिए प्रांत \(\left[\frac{1}{2},\frac{7}{3}\right]\) है।
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