For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-6

Key Concepts

Function Operations

Function operations involve combining two or more functions to create a new function. In this case, (ƒ-g)(x) represents the subtraction of function g(x) from function ƒ(x). Understanding how to perform operations like addition, subtraction, multiplication, and division on functions is essential for manipulating and analyzing them.

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. For linear functions like ƒ(x) = 3x + 4 and g(x) = 2x - 6, the domain is typically all real numbers, unless specified otherwise. Identifying the domain is crucial for understanding the behavior and limitations of the function.

Linear Functions

Linear functions are polynomial functions of degree one, represented in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. In this question, both ƒ(x) and g(x) are linear functions, which means their graphs are straight lines. Recognizing the characteristics of linear functions helps in performing operations and understanding their graphical representations.