The domain and range of a composite function f(g(x)) is where the domain and range of f(x) and g(x) overlap.
The domain of f(x) is (-∞, ∞). The domain of g(x) is also (-∞, ∞).
Thus, the domain of f(g(x)) is (-∞, ∞) ∩ (-∞, ∞), or just (-∞, ∞).
The range of f(x) is [0, ∞). That's because the absolute value is always positive. The range of g(x) is (-∞, ∞).
Thus, the range of f(g(x)) is [0,∞) ∩ (-∞, ∞), or just [0, ∞).
