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If \(f(x)=x-3\), what is the value of the product of the functions, \((ff)(x)\)?यदि \(f(x)=x-3\) है, तो फलनों के गुणनफल \((ff)(x)\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2-6x+9\)\(x^2-6x+9\)
By the definition of the product of functions, \((ff)(x)=f(x)\cdot f(x)\). Hence, \((ff)(x)=(x-3)(x-3)=(x-3)^2=x^2-6x+9\), so option C is correct. Option A results from adding \(f(x)\) to itself, not from multiplying the functions. Exam tip: interpret \((fg)(x)\) as \(f(x)g(x)\), whereas \((f+g)(x)\) means \(f(x)+g(x)\).फलनों के गुणनफल की परिभाषा के अनुसार \((ff)(x)=f(x)\cdot f(x)\)। इसलिए \((ff)(x)=(x-3)(x-3)=(x-3)^2=x^2-6x+9\), अतः विकल्प C सही है। विकल्प A \(f(x)+f(x)\) से प्राप्त होता है, गुणनफल से नहीं। परीक्षा-युक्ति: \((fg)(x)\) को \(f(x)g(x)\) और \((f+g)(x)\) को \(f(x)+g(x)\) के रूप में पहचानें।
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