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, ∞).