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If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are given by (f(x)=x+1), (g(x)=2x), which statement about ((f\circ g)(x)) and ((g\circ f)(x)) is correct?यदि (f:\mathbb{R}\to\mathbb{R}) और (g:\mathbb{R}\to\mathbb{R}) में (f(x)=x+1), (g(x)=2x), तो ((f\circ g)(x)) और ((g\circ f)(x)) के बारे में सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ((f\circ g)(x)=2x+1) and ((g\circ f)(x)=2x+2)((f\circ g)(x)=2x+1) और ((g\circ f)(x)=2x+2)
Step 1: (f(g(x))=f(2x)=2x+1). Step 2: (g(f(x))=g(x+1)=2x+2). Step 3: Composition of functions is not generally commutative.चरण 1: (f(g(x))=f(2x)=2x+1)। चरण 2: (g(f(x))=g(x+1)=2x+2)। चरण 3: फलनों का संयोजन सामान्यतः क्रमविनिमेय नहीं होता।
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