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}.