# Let A = (12, 13, 14, 15, 16, 17)

Question:

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.

Solution:

Given:

A ={12, 13, 14, 15, 16, 17}

f : A →  be defined by f (x) = the highest prime factor of x.

(12) = the highest prime factor of 12 = 3

(13) = the highest prime factor of 13 = 13

(14) = the highest prime factor of 14 = 7

f (15) = the highest prime factor of 15 = 5

(16) = the highest prime factor of 16 = 2

(17) = the highest prime factor of 17 = 17

The range of $f$ is the set of all $f(x)$, where $x \in A$.

Therefore,

range  of  f  = {2, 3, 5, 7, 13, 17}.