Question

# Let A = [9, 10, 11, 12, 13] and let f : A → N be defined by f(n) = the highest prime factor of n. Find the range of f.

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Solution

## Given: A ={9, 10, 11, 12, 13} f : A → N be defined by f (n) = the highest prime factor of n. f (9) = the highest prime factor of 9 = 3 f (10) = the highest prime factor of 10 = 5 f (11) = the highest prime factor of 11 = 11 f (12) = the highest prime factor of 12 = 3 f (13) = the highest prime factor of 13 = 13 The range of f is the set of all f (n), where $n\in A$. Therefore, range of f = {3, 5, 11, 13}

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