We can take those y's (outputs from our first function) and make those the x's (or inputs) of our inverse function, and we get the original inputs we started with.įunctions really do, and then we'll think about the idea ofĪn inverse of a function. The x's (or inputs) for our first function produce y's (outputs) from our first function. Now we take those y's and we make them our x values (or inputs) into function g and we should get our original 0, 1, and 2. 3, and -1 as the corresponding y's (try it yourself). We put in an x=0, 1, and 2 in function f, and we get, -5, You take the original function, switch all of the y's for x's and the x's for y's, and then you resolve it for y.įor example: if our original function f is y=2x-5, then we would switch the y's and x's to get x=2y-5. and that's exactly how you solve for the inverse function, g. If we think about it that way, then for the inverse of the f function (call it 'g', maybe), we should be able put IN the values that came OUT of function f as our y's, and get the same x values we put IN to f to get the y's originally.īut that is kind of like we switched the x's and y's in our f function….
So, for some function f, X goes in, and Y comes out. Then the function does some "stuff" and we get out a value called y.
For example, we take a value, called x, and that is what we put into the function. We sometimes think about functions as an input and an output. If you are trying to invert a function, one way to do it is to switch the positions of all of the variables, and resolve the function for y.
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