Question

Let $f:N-\left\{1\right\}\to N$ be defined by $f\left(x\right)$ = the highest prime factor of $n$. Show that $f$ is not onto. Find range of $f$

Answer 1

$f:N-1=N$

$f\left(x\right)=$ highest prime factor of $n$

$f$ is not obviously onto because a set of natural numbers is not equal to the set of prime numbers, also set of prime numbers is a subset of the natural number set.

range of '$f$' is set prime numbers