Let A ⊂ B ⊂ R, let f : B → R and let g be the restriction of f to A (that is, g(x) = f(x) for x ∈ A).
(a) If f is continuous at c ∈ A, show that g is continuous at c.
(b) Show by example that if g is continuous at c, it need not follow that f is continuous at c.