$x_n=(-1)^n$ and $f(x)=x^3$
does the sequence $f(x_n)$ converge(to anything)? I know $x_n$ doesn't converge to anything. is $f(x_n)=x_nx_nx_n$?
$f(x_n)=(x_n)^3=[(-1)^n]^3=[(-1)^3]^n=(-1)^n$