Given functions f and g, find (a)(ƒ∘g)(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, (ƒ∘g)(x) means applying g first and then applying f to the result of g. This process is essential for evaluating composite functions and understanding how they interact.

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 finding the domain of a composite function, it is crucial to consider the domains of both individual functions and any restrictions that may arise from the composition process.

Polynomial Functions

Polynomial functions are expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. In this question, g(x) = x^4 + x^2 - 4 is a polynomial function, and understanding its behavior, such as roots and end behavior, is important for determining the overall characteristics of the composite function.