Lecture 6 Inverse Functions In this section we will discuss how to nd the inverse function of a function f(x); namely a function that takes an output of f(x) and retu. ns the corresponding …

Objectives: Decide whether a function is one-to-one and, if it is, find its inverse. Use the horizontal line test to determine whether a function is one-to-one. Find the equation of the inverse of a …

The purpose of this lesson is to further develop undergraduates’ conceptual understanding of the relationship between a function and its inverse function and apply this understanding to find …

Once we have a one-to-one function, we can evaluate its inverse at specific inverse function inputs or construct a complete representation of the inverse function in many cases.

What is important to understand about the inverse function is that it is obtained by solving for the independent variable, then replacing it with y, to create a function that is also a function of x …

When a function has an inverse A function has an inverse exactly when it is both one-to-one and onto. This will be explained in more detail during lecture.

Finding Inverses Find an equation for the inverse for each of the following relations. 3. y 3 x 2 4. y 5 x 7 5. y 12 x 3