let f(x)=|x| and g(x)=x+2. what are the domain and range of (f o g)(x)

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, ∞).