Find inverses of polynomial, radical, and rational functions

The  exercise appears under the Algebra I Math Mission and Algebra II Math Mission. This exercise practices finding the formula of the inverse function of a given function algebraically.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the inverse of the rational function: This problem has a rational function. The student is asked to type the correct inverse function as an expression in in the text box.Find inverses of polynomial, radical, and rational functions.PNG
 * 2) Find the inverse of the polynomial function: This problem has a polynomial function. The student is asked to type the correct inverse function as an expression in in the text box.Find inverses of polynomial, radical, and rational functions2.PNG


 * 1) Find the inverse of the radical function: This problem has a radical function. The student is asked to type the correct inverse function as an expression in in the text box.Find inverses of polynomial, radical, and rational functions3.PNG

Strategies
Knowledge of the process involved to find inverse function is encouraged to ensure success on this exercise.
 * 1) If a function contains the point $$(a,b)$$ the inverse of that function contains the point $$(b,a)$$.
 * 2) If students swap the position of x and y in the equation, they will get the inverse relationship.
 * 3) It is important in mathematics to have a way of "undoing" operations so that equations can be solved with advanced mathematical operations and procedures. Inverses are the way to do this generally.

Real-life Applications

 * 1) Money as a function of time. One never has more than one amount of money at any time because they can always add everything to give one total amount. By understanding how their money changes over time, they can plan to spend their money sensibly. Businesses find it very useful to plot the graph of their money over time so that they can see when they are spending too much.
 * 2) Temperature as a function of various factors. Temperature is a very complicated function because it has so many inputs, including: the time of day, the season, the amount of clouds in the sky, the strength of the wind, and many more. But the important thing is that there is only one temperature output when they measure it in a specific place.
 * 3) Location as a function of time. One can never be in two places at the same time. If they were to plot the graphs of where two people are as a function of time, the place where the lines cross means that the two people meet each other at that time. This idea is used in logistics, an area of mathematics that tries to plan where people and items are for businesses.