Question: Let (fn) be a sequence of functions that converges uniformly to f on A and that satisfies |fn (x)| < M for all n

Let (fn) be a sequence of functions that converges uniformly to f on A and that satisfies |fn (x)| < M for all n ∈ N and all x ∈ A. If g is continuous on the interval = (-M; M), show that the sequence (g o fn) converges uniformly to g o f on A.

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