Max & Min

Let $f(x)= x+ a \cos{x} \, (a>1)$ be defined on the domain $0\leq x\leq 2\pi$ . Which of the statements below is (are) correct?

a. Regardless of the value of $a,$ $f(x)$ has both maximum and minimum values.

b. $f(x)>0.$

c. When the minimum value of $f(x)$ is $0,$ the maximum value of $f(x)$ is $\pi.$