I'll be very thankful is someone will tell me where I'm wrong.(adsbygoogle = window.adsbygoogle || []).push({});

We know:

1) f is uniform continuous.

2) g is uniform continuous.

We want to prove:

fg(x) is uniform continuous.

proof:

from 1 we know -> for every |a-b|<d_0 exists |f(a)-f(b)|<e

from 2 we know -> for every |x-y|<d exists |g(x)-g(y)|<d_0

let a=g(x) and b=g(y) then

for every x,y |x-y|<d exists |fg(x)-fg(y)|<e.

Sorry for my poor formulation, English is not my mother tongue.

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# Uniform continuity of composite function

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