How to find continuity and Diffrentiability

Question

The real function  f(x) = cos (|x|) is

Answer 1

$cos|x|$ is same as $cosx$. (sinse cos(-x) = cos(x) or you can take the intuition that it will be symmetric to y-axis and compare that with the graph of cosx)

Hence the question is now reduced to $f(x) = cos(x)$ which is both continuous and differentiable everywhere.