Question: Let g : R R be continuous functions, defined on the whole the real axis. Question: Assume that g(x) a for x g(x) b for

Let g :R R be continuous functions, defined on the whole the real axis. Question: Assume that

g(x) a for x g(x) b for x

for two real numbers a and b. Explain that for every > 0 there exists a K > 0 such that

|g(x) g(y)|< x, y K .

Show that g is uniformly continuous.

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