Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises - Page 10: 42

$g \circ f=x^2-4$, $x \in \mathbb{R}$

We evaluate the composite function: $g \circ f=g(f(x))=g(|x|)=|x|^2-4=x^2-4$ Since $|x|^2=x^2$ (the absolute value is redundant because squaring makes the resulting value positive). The domain is the set of all real numbers, since the function is defined for all real number values of $x$.