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.

Given: A = {9,10,11,12,13}

f : A N be defined by f(n) = the highest prime factor of n.


Prime factor of 9 = 3


Prime factor of 10 = 2,5


Prime factor of 11 = 11


Prime factor of 12 = 2,3


Prime factor of 13 = 13


f(n) = the highest prime factor of n.


Hence,


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


As the range of f is the set of all f(n), where n Є A.


Thus, the range of f is: {3, 5, 11, 13}.


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