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If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are given by (f(x)=2x+1), (g(x)=x^2-1), what is ((f\circ g)(x))?यदि (f:\mathbb{R}\to\mathbb{R}) और (g:\mathbb{R}\to\mathbb{R}) में (f(x)=2x+1), (g(x)=x^2-1), तो ((f\circ g)(x)) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2x^2-1)(2x^2-1)
Step 1: ((f\circ g)(x)=f(g(x))). Step 2: Substitute (g(x)=x^2-1) into (f) to get (2(x^2-1)+1). Step 3: Simplifying gives (2x^2-1).चरण 1: ((f\circ g)(x)=f(g(x))) होता है। चरण 2: (g(x)=x^2-1) को (f) में रखने पर (2(x^2-1)+1) मिलता है। चरण 3: सरल करने पर (2x^2-1) आता है।
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