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Solution


Q.

The function f:N-{1}→N; defined by f(n) = the highest prime factor of n, is:                   [2024]
1 one-one only  
2 both one-one and onto  
3 neither one-one nor onto  
4 onto only  

Ans.

(3)

   Given, f:N-{1}→N

   f(n)=the highest prime factor of n

   For one-one: If n=4,f(n)=2.

   If n=8,f(n)=2  ∴f is not one-one.

   For onto : Range = All prime numbers

   Co-domain = Set of natural numbers

  ⇒ Range ≠ Co-domain  ∴f is not onto.