Let f: X -> Y and g: Y -> Z be uniformly continuous on X and Y, respectively.  Prove g ◦ f: X -> Y is uniformly continuous on X.

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Q: 4. Prove fx=x2+4 is not uniformly continuous on R

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Q: Suppose f,g: D -> R are uniformly continuous on D. Prove that f+g is uniformly continuous on D.

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Q: 3. Let f, g : D →R be continuous at c € D. Prove that fg is continuous at c.

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Q: Let f : R → R be a continuous function satisfying f(x + y) = f (x) · fG) for all x, y E R 1. Show…

A: solution of above question is given below