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Subjects
Class 12MathematicsRelations and FunctionsFunctionsMedium
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If (g\circ f) is one-one, which statement is definitely true about (f)?

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), so (f) is one-one.

Related tags

CompositionInjective FunctionTheoryMediumFunctionsRelations And FunctionsMathematicsClass 12 Mcq
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