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Subjects
Class 12MathematicsRelations and FunctionsOne-one functionMedium
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If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=\sqrt{x^2}), choose the correct statement about (f).

Answer and explanation

Correct answer: Not one-one

Step 1: (\sqrt{x^2}=|x|). Step 2: (f(2)=2) and (f(-2)=2), while (2\neq -2). Step 3: Treat (\sqrt{x^2}) as modulus while solving.

Related tags

Square-RootModulusNot-One-OneOne One FunctionRelations And FunctionsMathematicsClass 12 Mcq
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  1. 1Which statement is true for a one-one function?
  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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