Inverse Functions

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x³ or f(x) = (x+1)/(xֱ) for x ≠ 1.

• Determine whether or not a function has an inverse, and find the inverse if it exists.
• Understand that creating an inverse of a quadratic function requires a restricted domain.

Common Core: HSF-BF.B.4

Inverse Functions
Define an inverse function. Determine if a function as an inverse function. Determine inverse functions.

Ex 1: Find the Inverse of a Function
This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly.

Ex 2: Find the Inverse of a Function
This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly.<

Ex: Find the Inverse of a Rational Function
This video explains how to find the inverse of a rational function with x in both the numerator and denominator.



Ex: Find the Inverse of a Rational Function and an Inverse Function Value
This video explains how to find the inverse of a rational function with x in both the numerator and denominator. It also shows how to evaluate the inverse function.

Ex: Find the Inverse of a Square Root Function with Domain and Range
This video explains how to find the domain and range of a square root function, how to find the inverse of a square root function, and find the domain and range of the inverse function.



Inverse Functions - The Basics
All of the fundamental ideas of inverse functions are discussed. What exactly is an inverse function conceptually? Which functions have inverses? How do I graph inverse functions? What are the other basic relationships?

Wolfram Function Transformations and Inverses
This Demonstration explores the affects of function transformations on the graphs of some elementary functions. The "inverse" button sketches the inverse of a selected function, which may or may not be a function. With the "inverse" control checked, you can adjust the domain using the "xmin" and "xmax" sliders so that the inverse becomes a function.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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