Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Show that E∩F = {0} and f(E∩F) = {0}, while f(E) = f(F) = {y∊R : 0≤y≤1}. Hence f(E∩F) is a proper subset of f(E) ∩ f(F). What happens if 0 is deleted from the sets E and F?

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