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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