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If \(f(x)=x^2-1\) and \(g(x)=x^2+1\), what is the value of \((g-f)(x)\)?यदि \(f(x)=x^2-1\) और \(g(x)=x^2+1\) हैं, तो \((g-f)(x)\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 22
By the definition of the difference of two functions, \((g-f)(x)=g(x)-f(x)\). Hence, \((g-f)(x)=(x^2+1)-(x^2-1)=x^2+1-x^2+1=2\). Option B results from not handling the subtraction of the second bracket correctly. Exam tip: When subtracting a bracket, change the signs of every term inside it.फलनों के अंतर की परिभाषा के अनुसार \((g-f)(x)=g(x)-f(x)\)। इसलिए \((g-f)(x)=(x^2+1)-(x^2-1)=x^2+1-x^2+1=2\)। विकल्प B में \(x^2\) पदों का सही निरसन नहीं हुआ है। परीक्षा-टिप: दूसरे फलन को घटाते समय उसके कोष्ठक के अंदर के सभी चिह्न बदल दें।
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