Let's say I have
$f: X \to Y$ where $f(x) = x^2$
$g: Y \to Z$ where $ g(y) = \cos(y)$ and
$h: Z \to X$ where $h(z) = 2x-1$
If I take $ f \circ (g \circ h)$ I get $\cos^2(2x-1)$
What is the co-domain of this function? Is there some sort of rule for finding the co-domain? It's easy enough to find the domain and range but I'm not sure about the co-domain.