Let A = {6, 10, 11, 15, 12} and let f : A → N : f(n) is the highest prime factor of n. Find range (f).

Given, A = {6, 10, 11, 15, 12}

f : A → N : f(n) is the highest prime factor of n

(1) When n = 6, the highest prime factor of 6 is 3.

Hence, f(6) = 3.

(2) When n = 10, the highest prime factor of 10 is 5.

Hence, f(10) = 5.

(3) When n = 11, the highest prime factor of 11 is 11 as 11 itself is a prime number.Hence, f(11) = 11.

(4) When n = 15, the highest prime factor of 15 is 5.

Hence, f(15) = 5.

(5) When n = 12, the highest prime factor of 12 is 3.

Hence, f(12) = 3.

Hence range of f is { 3,5,11}.

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