Let A = {9, 10, 11, 12, 13} and let f : A → Z be a function given by

1.	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}.

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}.