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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=2x+1) and (g:\mathbb{R}\to\mathbb{R}), (g(x)=x^2), is (g\circ f) one-one?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=2x+1) और (g:\mathbb{R}\to\mathbb{R}), (g(x)=x^2), तो (g\circ f) एकैकी है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Not one-oneएकैकी नहीं है
Step 1: ((g\circ f)(x)=(2x+1)^2). Step 2: At (x=0) and (x=-1), the output is (1) both times. Step 3: The outer function (x^2) is not one-one on the whole real domain, so this composition is also not one-one here.चरण 1: ((g\circ f)(x)=(2x+1)^2)। चरण 2: (x=0) और (x=-1) रखने पर दोनों बार मान (1) आता है। चरण 3: बाहरी फलन (x^2) पूरे वास्तविक क्षेत्र पर एकैकी नहीं है, इसलिए संयोजन भी यहाँ एकैकी नहीं है।
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