Q. 125.0( 3 Votes )

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.

Answer :

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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