Question

Check the injectivity and surjectivity of the following function.

f : Z → Z given by f(x) = x² 

Answer 1

f : Z → Z given by f(x) = x² 

f(2) = 2² = 4 and f(– 2) = (– 2)² = 4

∴ f(2) = f(– 2) but 2 ≠ – 2

∴ f is not injective

2 ∈ Z but there is no x ∈ Z such that 2 = f(x) = x²

∴ f is not surjective

∴ f is neither injective nor surjective.