Question

Let f be the subset of Z x Z defined by f ={(ab,a +b):a,b ∈ z) Is f a function from Z to Z?

Answer 1

Given f = {(ab, a + b):a,b ∈ Z) 

If a = 1 and b = 4 = ab = 4 and a + b = 5 

∴ (4,5) ∈ f If a = 2 and b = 2 ⇒ ab = 4 and a + b = 4 

∴ (4,4) ∈ f

∴ The element 4 has two images, so f is not a function.