Relations and Functions (Class 12)

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

1. one-one only
2. neither one-one nor onto
3. onto only
4. both one-one and onto

Answer

(2) neither one-one nor onto

Solution

f(2)=2 and f(4)=2 ⇒ two inputs, same image ⇒ not one-one

∵ f(n) is always a prime, non-primes like 1, 4, 6 are never images ⇒ range ≠ N ⇒ not onto

∴ f is neither one-one nor onto

Answer: (2)