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If \(f(x)=x\) and \(g(x)=x^2\), then \((f+g)(x)\) is equal to which expression?यदि \(f(x)=x\) और \(g(x)=x^2\) हैं, तो \((f+g)(x)\) किसके बराबर है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x+x^2\)\(x+x^2\)
By the definition of the sum of two functions, \((f+g)(x)=f(x)+g(x)\). Therefore, \((f+g)(x)=x+x^2\). The option \(x^3\) represents \(f(x)g(x)\), the product of the function values, not their sum. Exam tip: For \((f+g)(x)\), add the values of the two functions at the same input.फलनों के योग की परिभाषा के अनुसार \((f+g)(x)=f(x)+g(x)\)। इसलिए \((f+g)(x)=x+x^2\)। विकल्प \(x^3\), \(f(x)g(x)\) अर्थात् फलनों के गुणन को दर्शाता है, योग को नहीं। परीक्षा-टिप: \((f+g)(x)\) में दोनों फलनों के मान जोड़े जाते हैं।
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