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If \(f(x)=x^2+2x+1\) and \(g(x)=x+1\), where \(g^2\) denotes \((g(x))^2\), what is the value of \((f-g^2)(x)\)?यदि \(f(x)=x^2+2x+1\) और \(g(x)=x+1\) हैं तथा \(g^2\) से आशय \((g(x))^2\) है, तो \((f-g^2)(x)\) का मान क्या है?
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For algebraic operations on functions, \(g^2(x)\) means \((g(x))^2\), not the composition \(g(g(x))\). Thus, \(g^2(x)=(x+1)^2=x^2+2x+1\). Therefore, \((f-g^2)(x)=(x^2+2x+1)-(x^2+2x+1)=0\). Option B results from an incorrect subtraction of only some terms. Exam tip: distinguish the pointwise square \(g^2\) from the composition \(g\circ g\).फलनों के बीजीय संक्रिया में \(g^2(x)\) का अर्थ \((g(x))^2\) होता है, न कि \(g(g(x))\)। अतः \(g^2(x)=(x+1)^2=x^2+2x+1\)। इसलिए \((f-g^2)(x)=(x^2+2x+1)-(x^2+2x+1)=0\)। विकल्प B में केवल कुछ पदों का गलत घटाव हुआ है। परीक्षा-युक्ति: फलनों के लिए \(g^2\) और संयोजन \(g\circ g\) को अलग-अलग पहचानें।
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