Question

EXAMPLE 15 Let f:N – (1) ► N be defined by, f(n) = the highest prime factor of n.
Show that f is neither one-one nor onto. Find the range of f.​

Answer 1

Answer:

Let f:N – (1) ► N be defined by

f(n) = the highest prime factor of n

ONE-ONE ::

Since f(14) = 7 & f(7) = 7

Which leads to f(14)=f(7) but 14#7

SO f is not one-one

ONTO ::

6 € N

but 6 has no pre-image Since 6 is not a prime

So f is not onto

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Answer 2

Answer:

f is neither one-one nor onto