The function $$f : \mathbb{N} - \{1\} \rightarrow \mathbb{N}$$; defined by $$f(n) =$$ the highest prime factor of $$n$$, is :

$$f : \mathbb{N} - \{1\} \to \mathbb{N}$$ where $$f(n)$$ = highest prime factor of $$n$$.

One-one? No. $$f(4) = 2$$ and $$f(8) = 2$$. Different inputs give the same output.

Onto? We need every natural number to be a highest prime factor of some $$n$$. But $$f(n)$$ is always a prime number, so $$1, 4, 6, 8, ...$$ (non-primes) are never in the range. So not onto.

The function is neither one-one nor onto. The answer corresponds to Option (4).