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If the real-valued function \(f(x)=x-2\), what is \((ff)(x)\) when \((ff)\) denotes the product of the functions?यदि वास्तविक फलन \(f(x)=x-2\) है, तो फलनों के गुणनफल के रूप में \((ff)(x)\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2-4x+4\)\(x^2-4x+4\)
By the definition of the product of functions, \((ff)(x)=f(x)\cdot f(x)\). Therefore, \((ff)(x)=(x-2)(x-2)=(x-2)^2=x^2-4x+4\), so option A is correct. Option B represents \(2f(x)\), not the product \(f(x)f(x)\). In an exam, distinguish \((ff)(x)\) from \(f(f(x))\), which denotes composition.फलनों के गुणनफल की परिभाषा के अनुसार \((ff)(x)=f(x)\cdot f(x)\)। अतः \((ff)(x)=(x-2)(x-2)=(x-2)^2=x^2-4x+4\), इसलिए विकल्प A सही है। विकल्प B केवल \(2f(x)\) के बराबर है, गुणनफल के नहीं। परीक्षा में \((ff)(x)\) को \(f(f(x))\) से अलग पहचानें; \(f(f(x))\) फलनों का संयोजन होता है।
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