Question

Let A be the set of two positive integers. Let f : A --> set of positive integers be defined by
f(n) = p, where p is the highest prime factor of n
If range of f = {3}. Find set A. Is A uniquely determined?

Answer 1

Given range of function is {3}.
So p=3 which states the highest prime factor of number in the set should be 3.
Now 3,6,9 has highest prime factors as 3.
Set A can have values
3,6,9.
So A={3,6,9}
As set A has three values it cannot be uniquely determined.