## Calculus (3rd Edition)

Since for any $x\in R$, then $x^2\in R$, and by Theorem 3 $f(x)= \cos x^2$ is a continuous function.
We are given the function $f(x)= \cos x^2$. Since for any $x\in R$, then $x^2\in R$, and by Theorem 3 $f(x)= \cos x^2$ is a continuous function.