Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = th

1.	Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
Answer» A = {9, 10, 11, 12, 13} f: A → N is defined as f(n) = The highest prime factor of n Prime factor of 9 = 3 Prime factors of 10 = 2, 5 Prime factor of 11 = 11 Prime factors of 12 = 2, 3 Prime factor of 13 = 13 ∴ f(9) = The highest prime factor of 9 = 3 f(10) = The highest prime factor of 10 = 5 f(11) = The highest prime factor of 11 = 11 f(12) = The highest prime factor of 12 = 3 f(13) = The highest prime factor of 13 = 13 The range of f is the set of all f(n), where n ∈ A. ∴ Range of f = {3, 5, 11, 13}

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

Answer»

A = {9, 10, 11, 12, 13} f: A → N is defined as f(n) = The highest prime factor of n

Prime factor of 9 = 3

Prime factors of 10 = 2, 5

Prime factor of 11 = 11

Prime factors of 12 = 2, 3

Prime factor of 13 = 13

∴ f(9) = The highest prime factor of 9 = 3

f(10) = The highest prime factor of 10 = 5

f(11) = The highest prime factor of 11 = 11

f(12) = The highest prime factor of 12 = 3

f(13) = The highest prime factor of 13 = 13

The range of f is the set of all f(n), where n ∈ A.

∴ Range of f = {3, 5, 11, 13}

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