JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Sets Relations and Functions

$f(2)=2$ and $f(4)=2$ (since $4=2^2$ has highest prime factor $2$), so two different inputs share an output — $f$ is not one-one.

No natural number has $4$ itself as its highest prime factor (since $4$ is not prime), so $4$ has no pre-image — $f$ is not onto either. $f$ is neither one-one nor onto.