Tip:A–D to answerE for explanationV for videoS to reveal answer
The function f:N−{1}→N, defined by f(n) is the highest prime factor of n, is:
- A.
neither one-one nor onto
(Correct Answer) - B.
one-one only
- C.
both one-one and onto
- D.
onto only
Correct Answer: neither one-one nor onto
Explanation
f:N∖{1}→N
f(n)= the highest prime factor of n
∵ f(2)=f(4)=2
But 2=4
⇒f is not one-one
There is no such n in the codomain such that f(x)=1
So, f is not onto
Explanation
f:N∖{1}→N
f(n)= the highest prime factor of n
∵ f(2)=f(4)=2
But 2=4
⇒f is not one-one
There is no such n in the codomain such that f(x)=1
So, f is not onto
