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If \(f(x)=x+1\), \(g(x)=x-1\), and \((af+bg)(x)=5x+1\), what is the value of \(a+b\)?यदि \(f(x)=x+1\), \(g(x)=x-1\) और \((af+bg)(x)=5x+1\) है, तो \(a+b\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 55
\((af+bg)(x)=a f(x)+b g(x)=a(x+1)+b(x-1)=(a+b)x+(a-b)\). Comparing this with \(5x+1\) gives \(a+b=5\) and \(a-b=1\). Therefore, the correct answer is 5. In such questions, compare coefficients of corresponding powers, especially the coefficient of \(x\).\((af+bg)(x)=a f(x)+b g(x)=a(x+1)+b(x-1)=(a+b)x+(a-b)\)। इसकी तुलना \(5x+1\) से करने पर \(a+b=5\) और \(a-b=1\) मिलता है। इसलिए सही उत्तर 5 है। परीक्षा में ऐसे प्रश्नों में समान घात वाले पदों, विशेषकर \(x\) के गुणांक, की तुलना सीधे करें।
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