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 \( \pi. \)

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