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If \(f(x)=3x^2\) and \(g(x)=2x^2+1\), then \((f+g)(x)\) is equal to which of the following?यदि \(f(x)=3x^2\) और \(g(x)=2x^2+1\) हैं, तो \((f+g)(x)\) किसके बराबर है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(5x^2+1\)\(5x^2+1\)
The sum of two functions is found pointwise: \((f+g)(x)=f(x)+g(x)=3x^2+(2x^2+1)=5x^2+1\). Hence, option A is correct. Option B incorrectly combines the expressions as if they were multiplied and also changes the powers. Exam tip: when adding like terms, add their coefficients and keep the common power unchanged.फलनों का योग बिंदुवार किया जाता है: \((f+g)(x)=f(x)+g(x)=3x^2+(2x^2+1)=5x^2+1\)। इसलिए विकल्प A सही है। विकल्प B में गुणा और घातों का गलत प्रयोग किया गया है। परीक्षा-युक्ति: समान घात वाले पदों के गुणांक जोड़ें, घात नहीं।
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