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If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are both one-one, which statement about (g\circ f) is correct?यदि (f:\mathbb{R}\to\mathbb{R}) और (g:\mathbb{R}\to\mathbb{R}) दोनों एकैकी हैं, तो (g\circ f) के बारे में सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is always one-oneयह हमेशा एकैकी है
Step 1: Suppose ((g\circ f)(x_1)=(g\circ f)(x_2)). Step 2: Since (g) is one-one, (f(x_1)=f(x_2)); since (f) is one-one, (x_1=x_2). Step 3: The composition of one-one functions is one-one.चरण 1: मान लें ((g\circ f)(x_1)=(g\circ f)(x_2))। चरण 2: (g) एकैकी है, इसलिए (f(x_1)=f(x_2)); फिर (f) एकैकी है, इसलिए (x_1=x_2)। चरण 3: एकैकी फलनों का संयोजन फिर एकैकी होता है।
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