Final answer:
The composite function f ∘ g is (x - 1)² + 2, and the domain of f ∘ g is all real numbers.
Step-by-step explanation:
To find the composite function f ∘ g, we need to evaluate f(g(x)). Given that f(x) = x² + 2 and g(x) = x - 1, we substitute g(x) into f(x). Therefore, f(g(x)) = f(x - 1) = (x - 1)² + 2.
To find the domain of f ∘ g, we need to consider any restrictions on x for g(x) and then any subsequent restrictions for f(g(x)). The function g(x) = x - 1 is defined for all real numbers, so its domain is all real numbers. Applying g(x) to f(x), we still have a quadratic function, which is also defined for all real numbers. Thus, the domain of f ∘ g is all real numbers.