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If \(f(x)=\frac{2}{x}\) and \(g(x)=x^2\), and \((fg)(x)=f(x)g(x)\), what is the value of \((fg)(3)\)?यदि \(f(x)=\frac{2}{x}\) और \(g(x)=x^2\) हैं, तथा \((fg)(x)=f(x)g(x)\), तो \((fg)(3)\) का मान क्या है?
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Correct answer:सही उत्तर: 66
For the product of two functions, \((fg)(3)=f(3)g(3)\). Here, \(f(3)=\frac{2}{3}\) and \(g(3)=3^2=9\), so \((fg)(3)=\frac{2}{3}\times9=6\). Option C is only \(f(3)\), while option B is only \(g(3)\). Exam tip: interpret \((fg)(a)\) as \(f(a)g(a)\), not as the composition of the functions.फलनों का गुणनफल लेने पर \((fg)(3)=f(3)g(3)\)। यहाँ \(f(3)=\frac{2}{3}\) और \(g(3)=3^2=9\), इसलिए \((fg)(3)=\frac{2}{3}\times 9=6\)। विकल्प C केवल \(f(3)\) का मान है, जबकि विकल्प B केवल \(g(3)\) का मान है। परीक्षा-युक्ति: \((fg)(a)\) को \(f(a)g(a)\) समझें, इसे फलनों की रचना न मानें।
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