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Class 12MathematicsRelations and FunctionsOne-one functionExpert
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If (f:A\to B) is one-one and (S\subseteq A), which statement is correct about the restricted function (f|_S:S\to B)?

Answer and explanation

Correct answer: It will also be one-one

Step 1: (f) sends distinct inputs of (A) to distinct images. Step 2: (S) is only a smaller part of (A), so distinct elements of (S) also keep distinct images. Step 3: A restriction of a one-one function is also one-one.

Related tags

Restriction Of FunctionOne-OneSubsetConceptualOne One FunctionRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  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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  4. 4If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=7), what type of function is (f)?
  5. 5If (f:\mathbb{R}\to[0,\infty)) and (f(x)=|x|), what type of function is (f)?
  6. 6If (f:\mathbb{R}\to(0,\infty)) and (f(x)=e^x), what type of function is (f)?
  7. 7If (f:(0,\infty)\to\mathbb{R}) and (f(x)=\log x), which statement about (f) is correct?
  8. 8If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=3x-5), what follows from (f(a)=f(b))?
  9. 9Which example proves that (f(x)=x^2+1) is not one-one on real numbers?
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