Suppose that $f(x) = g \big( h(x) \big)$. In each part, based on one of the functions provided, find a formula for the other formula such that their composition yields $f(x) = g \big( h(x) \big)$. Be sure to play close attention to the order of composition. $$f(x) = \cos{\big( 4 + \cos{(x)}\big)}$$

(a) If $g(x) = \cos{(x)}$, then
$h(x) =$

(b) If $h(x) = \cos{(x)}$, then $g(x) =$