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i have been working on problems with continuity and i have come across some question in which i understand generally what i have to do but i just dont know where to start and how to put it together

a function f:R->R is said to be periodic if there exists a number k>0 such that

f(x+k)=f(x) for all x an element of R. suppose that f:R->R is continuous and periodic. Prove that f is bounded and uniformly continuous on R.

also

let f:R-->R be a function which satisfies the conditions

f(x+y)=F(x)+f(y)

and

f(-x)=-f(x) for al x znd y an element of R

suppose that f is continuous at 0 show that f is continuous at every point in R

please help

Steven

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# Problems with continuity

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