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