In Exercises 31–50, find fg and determine the domain for each function. f(x) = x -5, g(x) = 3x²

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, fg means f(g(x)), which requires substituting g(x) into f(x). Understanding how to perform this substitution is crucial for finding the composite function.

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 essential to consider the domains of both individual functions and any restrictions that may arise from the composition process.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, typically expressed in the form g(x) = ax² + bx + c. In this problem, g(x) = 3x² is a quadratic function, and understanding its properties, such as its shape and behavior, is important for analyzing the composition with f(x).