In Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = 2/(x+3), g(x) = 1/x

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, (f o g)(x) means applying g first and then applying f to the result of g. Understanding how to correctly perform this operation is essential for solving the problem.

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 is influenced by the domains of the individual functions. Identifying restrictions, such as division by zero, is crucial for determining the overall domain of f o g.

Rational Functions

Rational functions are ratios of polynomials, and they can have specific restrictions based on their denominators. In this problem, both f(x) and g(x) are rational functions, which means we need to consider where their denominators are zero to avoid undefined values. This understanding is key to finding the domain of the composed function.