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If (f(x)=x^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) और (g(x)=x+1), 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: They are not always equalदोनों हमेशा समान नहीं हैं
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: These expressions are generally not equal, so order matters.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: दोनों व्यंजक सामान्यतः समान नहीं हैं, इसलिए क्रम का ध्यान रखें।
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