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If (f:\mathbb{R}\to\mathbb{R}) is an odd function and (g:\mathbb{R}\to\mathbb{R}) is an even function, which statement about (g\circ f) is correct?यदि (f:\mathbb{R}\to\mathbb{R}) विषम फलन है और (g:\mathbb{R}\to\mathbb{R}) सम फलन है, तो (g\circ f) के बारे में कौन सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is an even functionयह सम फलन है
Step 1: ((g\circ f)(-x)=g(f(-x))). Step 2: Since (f) is odd, (f(-x)=-f(x)); since (g) is even, (g(-f(x))=g(f(x))). Step 3: Therefore (g\circ f) is even.चरण 1: ((g\circ f)(-x)=g(f(-x)))। चरण 2: (f) विषम है, इसलिए (f(-x)=-f(x)); और (g) सम है, इसलिए (g(-f(x))=g(f(x)))। चरण 3: इसलिए (g\circ f) सम फलन है।
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