Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions to create a new function. 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 resulting function.
Recommended video:
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 fg must consider the domain of g(x) and any restrictions imposed by f(x) after substitution.
Recommended video:
Domain Restrictions of Composed Functions
Linear Functions
Both f(x) = 2x + 3 and g(x) = x - 1 are linear functions, characterized by their constant rate of change and graphing as straight lines. Understanding the properties of linear functions, such as their slopes and intercepts, is essential for analyzing their composition and determining the overall behavior of fg.
Recommended video: