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If \(f(x)=x+6\) and \(g(x)=x-6\), what is the simplified form of \((fg)(x)\)?यदि \(f(x)=x+6\) और \(g(x)=x-6\) हैं, तो \((fg)(x)\) का सरल रूप क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2-36\)\(x^2-36\)
The product of two functions is defined by \((fg)(x)=f(x)g(x)\). Hence, \((fg)(x)=(x+6)(x-6)=x^2-6^2=x^2-36\). Option B incorrectly suggests a sum-of-squares pattern, whereas this is a product of conjugate binomials. Exam tip: recognize the identity \((a+b)(a-b)=a^2-b^2\).दो फलनों का गुणनफल \((fg)(x)=f(x)g(x)\) होता है। इसलिए \((fg)(x)=(x+6)(x-6)=x^2-6^2=x^2-36\)। विकल्प B में योग-संबंधी रूप लिया गया है, जबकि यहाँ गुणनफल है। परीक्षा-टिप: \((a+b)(a-b)=a^2-b^2\) सर्वसमिका पहचानें।
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