I badly need help with a question.

Just to start of by defining the functions.

$f: \mathbb{Q}\rightarrow \mathbb{R}$ where $f(x) = 0.2\cos(\pi x)-7$.

$g: \mathbb{N}\rightarrow \mathbb{Q}$ where $g(x) = \frac{5x}2$

$h(x) = f(g(x))$ therefore $h(x)= 0.2\cos(\frac{5x\pi}2)-7$

a) What is the range of $h$?

b) What is the domain and codomain of $h$?

c) Is $h$ surjective (onto)?