- #1
steven187
- 176
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hello all,
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 don't 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
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 don't 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