$f(x)$ uniformly continuous at $(0,1)$ iff $g(x) = xf(x)$ is uniformly continuous at $(0,1)$?

Question

For $f(x)$ positive continuous function at $(0,1)$

Is it true or false that:

score 2 · Accepted Answer · answered Feb 19 '20 at 00:25

2

Take $f(x)={1\over x}$ is not uniformly continuous, gut $g(x)=xf(x)=1$ is uniformly continuous

answered Feb 19 '20 at 00:25

Tsemo Aristide

pretty simple, thank you for the help. Is there is a rule for arithmetic of uniformly continuous functions? lets say, if fx uniformly continuous and gx also, therefore, can i conclude about fx*gx that it is also uniformly continuous? – Alon Feb 19 '20 at 00:30
https://math.stackexchange.com/questions/345480/product-of-two-uniformly-continuous-functions-is-uniformly-continuous – Tsemo Aristide Feb 19 '20 at 00:44

1 Answers1