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The function f : N - 1 → N ; defined by f n = the highest prime factor of n , is :

Options

  1. Aboth one-one and onto
  2. Bone-one only
  3. Conto only
  4. Dneither one-one nor onto

Correct answer

D. neither one-one nor onto

Step-by-step solution

Given: f : N - 1 → N f ( n ) = The highest prime factor of n . Since, the only prime factor of 2 is 2 . ⇒ f ( 2 ) = 2 Also, factors of 4 are 1 , 2 and 4 . Out of these, the highest prime factor is 2 . ⇒ f ( 4 ) = 2 Similarly the highest prime factor of 16 , 32 , 64 , 128 , . . . is 2 So, the given function is many one. Now, no composite number will be image of any number. Example: 4 is not image of any element So, the given function f x is into. Hence many one and into Or, neither one-one nor onto.

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