Other function? Is there some other function, Is there a way to get back fromĨ to the 2, or is there a way to go back from Our domain, I input it into the function, we're getting Of this later on, especially in the linear algebra playlist,īut this is all the different values I can take on. Talk about this, and there's a much more rigorous discussion Of all of the possible values that my function can take on. We're inputting a number, 2,Īnd then the function is outputting the number 8. Now, when you apply theįunction, let's think about it means to take f of 2. Real, but we're making it a nice contained set here just Input any real number into this function. Sitting there, you have 3 over there, pretty much you could That I can input into that function, that is the domain. You might already beįamiliar with that notion. In a little bit more of an abstract sense. Is 2 times 3 plus 4, which is equal to 10. Is going to be equal to 2 times 2 plus 4, which is 4 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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