Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x+2, g(x)=x^4+x^2-4

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, (g∘ƒ)(x) means we first apply the function f to x, and then apply the function g to the result of f. Understanding how to correctly perform this operation is essential for solving the problem.

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. When composing functions, the domain of the resulting function is determined by the domain of the inner function and any restrictions imposed by the outer function. Identifying the domain is crucial to ensure that all inputs yield valid outputs.

Polynomial Functions

Polynomial functions are expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. In this problem, g(x) = x^4 + x^2 - 4 is a polynomial function. Understanding the properties of polynomial functions, such as their continuity and behavior, is important for analyzing the composition and its domain.