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If \(f(x)=x^2+3x+2\) and \(g(x)=x+1\), what is \(\left(\frac{f}{g}\right)(x)\) for \(x\ne -1\)?यदि \(f(x)=x^2+3x+2\) और \(g(x)=x+1\) हैं, तो \(x\ne -1\) के लिए \(\left(\frac{f}{g}\right)(x)\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x+2\)\(x+2\)
Factor the numerator as \(x^2+3x+2=(x+1)(x+2)\). Thus, \(\left(\frac{f}{g}\right)(x)=\frac{(x+1)(x+2)}{x+1}=x+2\), provided \(x\ne -1\). Option B is only \(g(x)\), not the quotient. Exam tip: always exclude values that make the denominator zero, even after cancellation.\(x^2+3x+2=(x+1)(x+2)\)। इसलिए \(\left(\frac{f}{g}\right)(x)=\frac{(x+1)(x+2)}{x+1}=x+2\), जहाँ \(x\ne -1\)। विकल्प B केवल \(g(x)\) है, भागफल नहीं। परीक्षा में भाग देने से पहले हर को शून्य करने वाले मान को डोमेन से हटाना याद रखें।
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