Determine if Two Functions are Inverses

In this lesson, we will learn how to determine if two functions are inverses of each other using function composition. To check if two functions are inverses, we evaluate both compositions. If f(g(x))=x and g(f(x))=x hold true for all values of x in the appropriate domains, we can conclude that the functions are indeed inverses. These conditions essentially indicate that the functions "undo" each other's actions, resulting in the original input value. The procedure of verifying function composition as a test for inverses arises from the properties and characteristics of inverse functions. When two functions are inverses, they essentially "reverse" the mapping of each other. By checking the composition, we are ensuring that applying one function followed by the other reproduces the original input.