The function f: N - 1 → N ; defined by f(n) = the highest prime...

Given: $f: N - { 1 } \to N$

$f ( n ) =$ The highest prime factor of $n$.

Since, the only prime factor of $2$ is $2$.

$⇒ f ( 2 ) = 2$

Also, factors of $4$ are $1, 2\text{and}4$. Out of these, the highest prime factor is $2$.

$⇒ f ( 4 ) = 2$

Similarly the highest prime factor of $16, 32, 64, 128, . . .$ is $2$

So, the given function is many one.

Now, no composite number will be image of any number.

Example: $4$ is not image of any element

So, the given function $f\left(x\right) is into.

Hence many one and into

Or, neither one-one nor onto.