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-5

Key Concepts

Function Addition

Function addition involves combining two functions by adding their outputs for each input value. For functions ƒ(x) and g(x), the sum (ƒ+g)(x) is defined as (ƒ+g)(x) = ƒ(x) + g(x). This operation is fundamental in algebra as it allows for the creation of new functions from existing ones.

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 polynomial functions like ƒ(x) = 3x + 4 and g(x) = 2x - 5, the domain is typically all real numbers, as there are no restrictions such as division by zero or square roots of negative numbers.

Linear Functions

Linear functions are functions of the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. They graph as straight lines and have constant rates of change. In this case, both ƒ(x) and g(x) are linear functions, which simplifies the process of finding their sum and understanding their behavior.