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Class 12MathematicsRelations and FunctionsOne-one functionExpert
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If (g\circ f) is one-one, which statement about (g) is the most accurate?

Answer and explanation

Correct answer: (g) must behave one-one at least on (f(A))

Step 1: In (g\circ f), (g) is used only on the range of (f). Step 2: (g) may not be one-one on its whole domain but can behave distinctly on (f(A)). Step 3: In composition, distinguish the used part from the whole domain.

Related tags

CompositionRange Of FunctionInjectivityExpertOne One FunctionRelations And FunctionsMathematicsClass 12 Mcq
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  9. 9Which example proves that (f(x)=x^2+1) is not one-one on real numbers?
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