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If \(f(x)=4x\) and \(g(x)=x+2\), find the value of \((fg)(2)\).यदि \(f(x)=4x\) और \(g(x)=x+2\) हैं, तो \((fg)(2)\) का मान ज्ञात कीजिए।
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Correct answer:सही उत्तर: 3232
Here, \((fg)(x)=f(x)g(x)\), so \(f(2)=8\) and \(g(2)=4\). Therefore, \((fg)(2)=8\times4=32\). The value 16 represents \(f(g(2))\), which is composition rather than multiplication. Exam tip: distinguish \((fg)(x)=f(x)g(x)\) from \((f\circ g)(x)\), which denotes composition.यहाँ \((fg)(x)=f(x)g(x)\) है, इसलिए \(f(2)=8\) और \(g(2)=4\)। अतः \((fg)(2)=8\times4=32\)। विकल्प 16, \(f(g(2))\) अर्थात संयोजन का मान है, गुणन का नहीं। परीक्षा-युक्ति: \((fg)(x)\) को \(f(x)g(x)\) और \((f\circ g)(x)\) को संयोजन समझें।
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