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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.

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