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Class 12MathematicsRelations and FunctionsOne-one functionExpert
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If (f:(-\infty,2]\to\mathbb{R}) and (f(x)=x^2), what is the correct statement about (f)?

Answer and explanation

Correct answer: (f) is not one-one because (f(1)=f(-1))

Step 1: The domain ((-\infty,2]) contains both (1) and (-1). Step 2: (1\neq-1), but (1^2=(-1)^2=1). Step 3: If the domain spreads on both sides of zero, (x^2) is not one-one.

Related tags

Square FunctionDomain RestrictionCounterexampleExpertOne One FunctionRelations And FunctionsMathematicsClass 12 Mcq
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  2. 2If (f(2)=5) and (f(3)=5), what can be said about (f)?
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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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