Functions-5

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Let A be the set of two positive integers. Let f : A → z+ (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?

Solution: It is given that the set A consists of two positive integers.

So, let A = {n, m}. Since range of f = {3}. Therefore, f(n) = 3 and f(m) = 3

=> Highest prime factors of n and m both are equal to 3.

=> (n = 3 and m = 6) or (n = 3 and m = 9) or (n = 3 and m = 12) or (n = 6 and m = 12) etc.

=> A = {3, 6} or A = {3,9} or A = {3,12} or A = {6, 12} etc.

Clearly, A is not uniquely determined.

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