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If (g\circ f) is one-one, which of the following statements is definitely true?यदि (g\circ f) एक-एक है, तो निम्न में से कौन सा कथन निश्चित रूप से सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f) is one-one(f) एक-एक है
Step 1: If (g\circ f) is one-one, the first function (f) cannot send two different inputs to the same value. Step 2: If (f(x_1)=f(x_2)), then ((g\circ f)(x_1)=(g\circ f)(x_2)), so (x_1=x_2). Step 3: If (g\circ f) is one-one, then (f) must be one-one.चरण 1: ((g\circ f)) की एक-एकता में पहला फलन (f) दो अलग आगतों को एक ही मान नहीं दे सकता। चरण 2: यदि (f(x_1)=f(x_2)), तो ((g\circ f)(x_1)=(g\circ f)(x_2)), इसलिए (x_1=x_2)। चरण 3: (g\circ f) एक-एक हो तो (f) जरूर एक-एक होता है।
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