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If \(f(x)=2x+1\) and \(g(x)=x-2\), what is the value of \((3f+2g)(x)\)?यदि \(f(x)=2x+1\) और \(g(x)=x-2\) हैं, तो \((3f+2g)(x)\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(8x-1\)\(8x-1\)
For a linear combination of functions, multiply each entire function by its coefficient: \((3f+2g)(x)=3f(x)+2g(x)=3(2x+1)+2(x-2)=6x+3+2x-4=8x-1\). Hence, option A is correct. Option B results from an incorrect sign in the constant term. In the exam, distribute each coefficient across every term of the corresponding function.फलनों के रैखिक संयोजन में पूरे फलनों को उनके गुणांकों से गुणा किया जाता है: \((3f+2g)(x)=3f(x)+2g(x)=3(2x+1)+2(x-2)=6x+3+2x-4=8x-1\)। अतः सही उत्तर A है। विकल्प B में स्थिर पद के चिह्न की गलती है। परीक्षा में प्रत्येक गुणांक को पूरे फलन के प्रत्येक पद से गुणा करना न भूलें।
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