(Composition of continuous functions) Let (S₁, d₁), (S2, d2), and (S3, d3) be metric spaces. Let f: S₁ S₂ and 9: S2 → S3. Show that if f is continuous at c € S₁ and g is continuous at b = f(c) € S₂ then the composition go f: S₁→ S3 is continuous at c.

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