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If (f(x)=x^2+2) and (g(x)=x-1), which statement about ((f\circ g)(x)) and ((g\circ f)(x)) is correct?यदि (f(x)=x^2+2) और (g(x)=x-1), तो ((f\circ g)(x)) तथा ((g\circ f)(x)) के बारे में सही कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: They are generally not equalदोनों सामान्यतः समान नहीं हैं
Step 1: ((f\circ g)(x)=f(x-1)=(x-1)^2+2). Step 2: ((g\circ f)(x)=g(x^2+2)=x^2+1). Step 3: The expressions are generally different, so order is important in composition.चरण 1: ((f\circ g)(x)=f(x-1)=(x-1)^2+2)। चरण 2: ((g\circ f)(x)=g(x^2+2)=x^2+1)। चरण 3: दोनों व्यंजक सामान्यतः अलग हैं, इसलिए संयुक्त फलन में क्रम महत्वपूर्ण है।
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