The domain and range can be the whole of the real numbers, or some subsets of these sets.
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The domain is from negative infinity to positive infinity. The range is from positive 2 to positive infinity.
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.
In trig, usually 0 to 2pi but it can be anything.
Domain is a set in which the given function is valid and range is the set of all the values the function takes
The domain and range of the composite function depend on both of the functions that make it up.