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If \(f(x)=x+1\), what is \((ff)(x)\) when \(ff\) denotes the product of the functions?यदि \(f(x)=x+1\) है, तो फलनों के गुणनफल के रूप में \((ff)(x)\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2+2x+1\)\(x^2+2x+1\)
For the product of functions, \((ff)(x)=f(x)\cdot f(x)=(x+1)(x+1)=(x+1)^2=x^2+2x+1\). Hence, option A is correct. Option B, \(f(x)+f(x)=2x+2\), represents the sum of the functions, not their product. In exams, carefully distinguish between \(ff\) and \(f+f\).फलनों के गुणनफल के लिए \((ff)(x)=f(x)\cdot f(x)=(x+1)(x+1)=(x+1)^2=x^2+2x+1\)। इसलिए विकल्प A सही है। विकल्प B, \(f(x)+f(x)=2x+2\), फलनों के योग को दर्शाता है, गुणनफल को नहीं। परीक्षा में \(ff\) और \(f+f\) के बीच का अंतर ध्यान से देखें।
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