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18 May, 17:52

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

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  1. 18 May, 20:59
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    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, ∞).
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