Have you ever been in a situation where you needed to make a U-Turn?
Well, I have lots of times… good thing there’s such a thing as Inverses!
What is an Inverse Function? and how can they help us?
Inverse Functions undo each other, like addition and subtraction or multiplication and division or a square and a square root, and help us to make mathematical “u-turns”.
In other words, Inverses, are the tools we use to when we need to solve equations!
This lesson is devoted to the understanding of any and all Inverse Functions and how they are found and generated.
The most important thing to note is that not all functions have inverses!
How can this be?
Well, an inverse only exists if a function is One-to-One.
Huh?
Okay, so as we already know from our lesson on Relations and Functions, in order for something to be a Function it must pass the Vertical Line Test; but in order to a function to have an inverse it must also pass the Horizontal Line Test, which helps to prove that a function is One-to-One.
And some textbooks will refer to this idea as a One-to-One mapping.
It is my hope that you will quickly see, finding Inverses is very straightforward, since all we have to do is switch our x and y variables!
And determining if a function is One-to-One is equally simple, as long as we can graph our function.
But there’s even more to an Inverse than just switching our x’s and y’s. As MathBits nicely points out, an Inverse and its Function are reflections of each other over the line y=x. This makes finding the domain and range not so tricky!
So, together, we will explore the world of Functions and Inverse, both graphically and algebraically, with countless examples and tricks.
Inverse Functions – Video
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