Show that the function defined by `f(x) = | cos x |`is a continuous function.

Explanation

Let's assume that `h(x)=cos (x)` and `g(x)=|x|`


So `f(x)=(g circ h)=|cos (x)|`


`Rightarrow` Let's prove that `h(x)=cos (x)` is continuous in it's domain.


Let `c` be a real number, put `{x}={c}+{h}`


So if `{x}={c}` then it means that `{h} -> 0`


`h(c)=cos (c)`


`lim _{x -> c} h(x)=lim _{x -> c} cos (x)`


Put `{x}={h}+{c}`


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