In Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 1/x, g(x)= 1/x

Key Concepts

Function Composition

Function composition involves combining two functions to create a new function. If f(x) and g(x) are two functions, the composition (fog)(x) means applying g first and then applying f to the result, expressed as f(g(x)). Understanding this concept is crucial for solving problems that require evaluating composite functions.

Evaluating Functions

Evaluating functions means substituting a specific value into a function to find its output. For example, if f(x) = 1/x, evaluating f(2) involves substituting 2 for x, resulting in f(2) = 1/2. This skill is essential for calculating the values of composite functions at given points.

Reciprocal Functions

Reciprocal functions are functions of the form f(x) = 1/x, which output the multiplicative inverse of the input. In this case, both f(x) and g(x) are reciprocal functions. Understanding their properties, such as asymptotes and behavior near zero, is important for analyzing the results of their compositions.