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Class 12MathematicsRelations and FunctionsOne-one functionExpert
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If (A={1,2,3,4}) and (f:A\to A) has (f(1)=3), (f(2)=3), (f(3)=4), (f(4)=1), what is correct about (f)?

Answer and explanation

Correct answer: It is not one-one

Step 1: Each domain element has an image, so it is a function. Step 2: Both (1) and (2) have image (3), so distinct inputs do not have distinct images. Step 3: Repeated images destroy one-one nature.

Related tags

Finite FunctionNot One-OneRepeated ImageOrdered MappingOne 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)?
  3. 3If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=2x+1), what type of function is (f)?
  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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