Question

The composition of the two functions, f(x) and g(x), is (f∘g)(x) = 2(x³ 5) 1. the domain for (f∘g)(x) is all real numbers, so the domain is (-[infinity], [infinity]).

Answer 1

The composition of two functions, f(x) and g(x), is found by substituting the expression for g(x) into f(x). The domain of (f∘g)(x) is the same as the domains of f(x) and g(x) if both functions have domains that include all real numbers.

Step-by-step explanation:

The composition of two functions, f(x) and g(x), denoted by (f∘g)(x), is found by substituting the expression for g(x) into f(x). In this case, (f∘g)(x) = 2((x³) - 5) + 1. To find the domain of (f∘g)(x), we need to consider the domains of f(x) and g(x). If both f(x) and g(x) have domains that include all real numbers, then the composition (f∘g)(x) will also have a domain of (-∞, ∞).