Inverse Functions (Complete Guide)

Learn about inverse functions in this complete guide. We discuss how to find the inverse of a function intuitively as well as algebraically. We discuss inverse function notation as well as the graphic interpretation of the inverse. In addition, know how to tell if the inverse of a function is a function as well as how to verify that functions are inverses of each other by using composition of functions. Lastly, we discuss how to restrict the domain of a function so that it's inverse will be a function.
0:40 What is a Function and Terminology
1:08 Some Examples of Inverse Functions
1:30 Introductory Example Find Inverse Given Coordinates
1:58 Intuitive Way of Finding the Inverse of y=2x-1
3:01 Algebraic Way of Finding the Inverse of y=2x-1
3:36 Looking at the Graph of a Function and it's Inverse
4:43 Find the Inverse of f(x)=(1/3)x+7
5:30 Notation for Writing the Inverse Function
5:49 More Challenging Example: Find Inverse of f(x)=(2x+3)/(x-4)
7:30 Vertical Line Test and Horizontal Line Test
9:20 Verifying Functions are Inverses Using Composition of Functions
12:00 Restrict the Domain of f(x)=2x^2 - 1 so that it is a Function
13:13 What Happens to the Domain & Range when you Find Inverse
Related Videos:
Find Inverse and State Domain Restriction
• Find Inverse and State...
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Good question! I’ve been tutoring math for many years so I’ve try to refine the explanations over the years to try and make it easier for students to grasp. You can use my videos and others on RUclips to give you inspiration and I’m sure you will develop your own preferred style of teaching. Hope that helps …

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Great, and thorough explanation. Thanks!

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[@thedeathofbirth0763]

Excellent introductory on inverse functions, my only criticism is that the adds are in a very inappropriate time. Please make sure they are played when you are computing and not when you are explaining .

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[@rafscn]

Hi, for the last question, what transformation does the denominator indicate? x + 1 clearly indicates that the function will be neither stressed or compressed, but rather shifted 1 unit to the left. On the other hand, I believe that the denominator is not associated with the “x”. So what transformation would it have?

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Shift, Stretch, Reflect Parent Functions by Identifying Transformations and Graph
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Finally 👍.
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You’re welcome!

[@memexo1751]

what is the inverse function of F^-1(T) when T={3, 5, 4} ? is it {-3, -5, -4}?

[@maricorgomez766]

How will I know which inverse function choose in restricting the domain

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Thank

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I need help with really hard word problems

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Regarding quadratics, completing the square, and factoring

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first