In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Key Concepts

Function Addition

Function addition involves combining two functions, f(x) and g(x), to create a new function, denoted as (f + g)(x) = f(x) + g(x). In this case, you will add the outputs of f(x) and g(x) for each input x, resulting in a new expression that represents the sum of the two functions.

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 the functions f(x) = √x and g(x) = x - 4, the domain must be determined by considering any restrictions, such as the requirement that the expression under the square root must be non-negative.

Square Root Function

The square root function, represented as f(x) = √x, is defined only for non-negative values of x, meaning x must be greater than or equal to zero. This characteristic affects the overall domain when adding it to another function, as the resulting function's domain will be influenced by the more restrictive domain of the square root function.