Final answer:
The domain of (f∘g)(x) is all real numbers, and the range is all positive real numbers.
Step-by-step explanation:
The composition of functions, denoted as f∘g, is the combination of two functions where the output of one function is used as the input for the other function. Using the given functions f(x)=ex and g(x)=x−3, we can find the composition as f∘g(x)=f(g(x)).
Substituting g(x) into f(x), we get f∘g(x)=e(g(x))=e(x−3).
The domain is the set of all valid input values. Since e(x) is defined for all real numbers, and x−3 is also defined for all real numbers, the domain of f∘g(x) is the set of all real numbers.
The range is the set of all possible output values. As e(x) is a positive exponential function, its range is (0,∞), meaning it takes on all positive real numbers. Therefore, the range of f∘g(x) is (0,∞).