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Class 12MathematicsRelations and FunctionsFunctionsHard
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If (f:A\to B) and (g:B\to C) are functions and (g\circ f) is one-one, which conclusion is definitely true?

Answer and explanation

Correct answer: (f) is one-one

Step 1: Suppose (f(a_1)=f(a_2)). Step 2: Then (g(f(a_1))=g(f(a_2))), so ((g\circ f)(a_1)=(g\circ f)(a_2)). Step 3: Since (g\circ f) is one-one, (a_1=a_2); therefore (f) is one-one.

Related tags

FunctionsCompositionOne-OneTheoryRelations And FunctionsMathematicsClass 12 Mcq
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  6. 6If (f={(1,2),(2,4),(3,6)}), what is the range of (f)?
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