Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover inverse functions.
1. Students have learned the basics of functions
2. Students have learned functional notation
4.. Students understand the domain and range of functions
Students are asked to evaluate two functions and to discover that the input of the first function is the output of the second function. They also discover that the output of the first function is the input of the second function. This investigation leads students to understand the definition of inverse functions. Students are asked to "undo" a function in order to understand how to find the inverse of a function. Finally, students are asked to give the definition of a function. Along the way students are led to discover that the result of thecomposition of two inverse functions is 1.