Let $\displaystyle f(x)=cosx+cos \pi x$

a) Show that $\displaystyle f(x)=2$ has a unique solution.

b) Show that f(x) is not periodic.

My proof so far:

Now, I realize that f(x) = 2 iff x=0 in this case, but will that be enough for a proof?

And since f(x) = 2 only once, then it cannot be periodic.