JEE Main 2024 — Functions Question with Solution

Given: $\mathrm{f}:\mathrm{N}-\left\{1\right\}\to \mathrm{N}$

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

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

$\Rightarrow f\left(2\right)=2$

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

$\Rightarrow f\left(4\right)=2$

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.