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If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are (f(x)=x^2), (g(x)=x+1), what is ((f\circ g)(x)-(g\circ f)(x))?यदि (f:\mathbb{R}\to\mathbb{R}) और (g:\mathbb{R}\to\mathbb{R}) के लिए (f(x)=x^2), (g(x)=x+1), तो ((f\circ g)(x)-(g\circ f)(x)) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2x)(2x)
Step 1: ((f\circ g)(x)=f(x+1)=(x+1)^2). Step 2: ((g\circ f)(x)=g(x^2)=x^2+1). Step 3: The difference is ((x+1)^2-(x^2+1)=2x).चरण 1: ((f\circ g)(x)=f(x+1)=(x+1)^2)। चरण 2: ((g\circ f)(x)=g(x^2)=x^2+1)। चरण 3: अंतर ((x+1)^2-(x^2+1)=2x) है।
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