Given A = {12, 13, 14, 15, 16, 17}

f : A → Z such that f(x) = highest prime factor of x.

A is the domain of the function f. Hence, the range is the set of elements f(x) for all x ∈ A.

We have f(12) = highest prime factor of 12

The prime factorization of 12 = 2² × 3

Thus, the highest prime factor of 12 is 3.

∴ f(12) = 3

We have f(13) = highest prime factor of 13

We know 13 is a prime number.

∴ f(13) = 13

We have f(14) = highest prime factor of 14

The prime factorization of 14 = 2 × 7

Thus, the highest prime factor of 14 is 7.

∴ f(14) = 7

We have f(15) = highest prime factor of 15

The prime factorization of 15 = 3 × 5

Thus, the highest prime factor of 15 is 5.

∴ f(15) = 5

We have f(16) = highest prime factor of 16

The prime factorization of 16 = 2⁴

Thus, the highest prime factor of 16 is 2.

∴ f(16) = 2

We have f(17) = highest prime factor of 17

We know 17 is a prime number.

∴ f(17) = 17

Thus, the range of f is {3, 13, 7, 5, 2, 17}.