Functions Question 3
Question 3 - 2024 (27 Jan Shift 1)
The function $f: N-{1} \rightarrow N$; defined by $f(n)=$ the highest prime factor of $n$, is :
(1) both one-one and onto
(2) one-one only
(3) onto only
(4) neither one-one nor onto
Show Answer
Answer (4)
Solution
$f: N-{1} \rightarrow N$
$f(n)=$ The highest prime factor of $n$.
$f(2)=2$
$f(4)=2$
$\Rightarrow$ many one
4 is not image of any element
$\Rightarrow$ into
Hence many one and into
Neither one-one nor onto.
