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JEE Main202228 Jun 2022Morning ShiftMathematicsFunctionsActual

Let a function f : ℕ → ℕ be defined by f n = 2 n , n = 2 , 4 , 6 , 8 , … . . n - 1 , n = 3 , 7 , 11 , 15 , … . . n + 1 2 , n = 1 , 5 , 9 , 13 , … . . then, f is

Options

  1. AOne-one and onto
  2. BOne-one but not onto
  3. COnto but not one-one
  4. DNeither one-one nor onto

Correct answer

A. One-one and onto

Step-by-step solution

For one value of n we will get only one corresponding value of f n , so f n is one-one Now, for n = 2 , 4 , 6 ⋯ ;   f n = 4 , 8 , 12 . . . for n = 3 , 7 , 11 ⋯ ;   f   n = 2 , 6 , 10 . . . for n = 1 , 5 , 9 ⋯ ;   f n = 1 , 3 , 5 , 7 . . . So range of f n is N Hence f n is onto

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