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. 

Answer 1

A = {9, 10, 11, 12, 13} f: A → N is defined as f(n) = The highest prime factor of n 

Prime factor of 9 = 3 

Prime factors of 10 = 2, 5 

Prime factor of 11 = 11 

Prime factors of 12 = 2, 3 

Prime factor of 13 = 13 

∴ 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 ∈ A. 

∴ Range of f = {3, 5, 11, 13}