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If (f(x)=x^2) and (g(x)=x+2), which statement about ((f\circ g)(x)) and ((g\circ f)(x)) is correct?यदि (f(x)=x^2) और (g(x)=x+2), तो ((f\circ g)(x)) और ((g\circ f)(x)) के बारे में सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ((g\circ f)(x)=x^2+2)((g\circ f)(x)=x^2+2)
Step 1: ((f\circ g)(x)=f(x+2)=(x+2)^2). Step 2: ((g\circ f)(x)=g(x^2)=x^2+2). Step 3: Composition of functions is generally not commutative.चरण 1: ((f\circ g)(x)=f(x+2)=(x+2)^2)। चरण 2: ((g\circ f)(x)=g(x^2)=x^2+2)। चरण 3: संयुक्त फलन सामान्यतः क्रमविनिमेय नहीं होता।
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