Q. 155.0( 5 Votes )

# Let A = {9, 10, 11, 12, 13} and let f : A → Z be a function given by f(n) = the highest prime factor of n. Find the range of f.

Answer :

Given A = {9, 10, 11, 12, 13}

f : A Z such that f(n) = the highest prime factor of n.

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

We have f(9) = highest prime factor of 9

The prime factorization of 9 = 32

Thus, the highest prime factor of 9 is 3.

f(9) = 3

We have f(10) = highest prime factor of 10

The prime factorization of 10 = 2 × 5

Thus, the highest prime factor of 10 is 5.

f(10) = 5

We have f(11) = highest prime factor of 11

We know 11 is a prime number.

f(11) = 11

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

Thus, the range of f is {3, 5, 11, 13}.

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