The function f: N-{1} rightarrow N defined by | vedclass

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(D) Given the function $f: N-\{1\} \rightarrow N$ where $f(n)$ is the highest prime factor of $n$.Check for one-one:$f(2) = 2$ (since the prime factor

Vedclass · Accepted Answer

neither one-one nor onto

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(D) Given the function $f: N-\{1\} ightarrow N$ where $f(n)$ is the highest prime factor of $n$.Check for one-one:$f(2) = 2$ (since the prime factor of $2$ is $2$)$f(4) = 2$ (since the prime factor of $4 = 2^2$ is $2$)Since $f(2) = f(4)$ but $2 
eq 4$,the function is not one-one (it is many-one).Check for onto:$A$ function is onto if the range equals the codomain $N$. The range of $f$ consists only of prime numbers.For example,$4 \in N$ (codomain),but there is no $n \in N-\{1\}$ such that $f(n) = 4$,because if $f(n) = 4$,then $4$ must be a prime factor of $n$,which is impossible as $4$ is not a prime number.Thus,the range is a subset of prime numbers,not equal to $N$.Therefore,the function is not onto (it is into).Conclusion: The function is neither one-one nor onto.

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

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