Is functions of cauchy sequences is also Cauchy? Recently i saw in some book that if a sequence is Cauchy then function of that sequence is also Cauchy.I have confusion about this. Please help me.

Let $\{a_n\}$ be a Cauchy sequence in R. $  \,\,\,  $ Then $\{a_n\}$ has a limit $a$. 
If $f:R→R$  is continuous on $x=a$,  then the sequence $\,\,\{f(a_n)\}\,\,$ converges to $\,\,f(a)$, thus it is Cauchy.
