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}.