# Let A = {12, 13, 14, 15, 16, 17} and f : A → Z be a function given by f(x) = highest prime factor of x. Find range of f.

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}.

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