In Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = = -x and g(x) = -x

Function composition involves combining two functions, where the output of one function becomes the input of another. For functions f and g, the composition f(g(x)) means applying g first and then f to the result. This process is essential for evaluating how two functions interact and can reveal properties such as inverses.

Inverse functions are pairs of functions that 'undo' each other. If f(x) is a function, its inverse, denoted as f⁻¹(x), satisfies the condition f(f⁻¹(x)) = x for all x in the domain of f. To determine if two functions are inverses, one must check if f(g(x)) = x and g(f(x)) = x for all x in their respective domains.

Linear functions are polynomial functions of degree one, typically expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. In this case, both f(x) = -x and g(x) = -x are linear functions with a slope of -1. Understanding their linearity helps in analyzing their behavior and relationships, particularly in terms of inverses.