Inverse Functions and graphing them HELP!!
I wasnt here friday so Im kind of lost on the inverse function homework. Im trying to figure it out but I dont have my book with me so can someone briefly summarize how to find inverses of functions, please?? Thanks so much!
posted by Elena at 4:58 PM
5 Comments:
(I'm sorry if it is too long)
To find inverse functions, the main point is to switch x and y.
For example, f(x)=4x, the first thing is to change f(x) to y. so the original function will be y=4x. In order to find the inverse function, you need to switch y and x(as I said before), change the function to x=4y, then solve for y, y=x/4, and that is the inverse function of f(x).
* if two function are inverse, them should make the following statements true. f^-1(f(x))=x, and f(f^-1(x))=x.
for graphing inverse functions, first you can graph the original function--y=4x. Find the coordinate of some point(it will be easier if you choose whole numbers). points (-4,-1)and(0,0) are on the graph, then you switch x-coordinate and y-coordinate, so you can get points (-1,-4) and (0,0), connect them, it will be the graph of this inverse function.
* The graph of your original function and the graph of your inverse function should be reflected to each other across the line y=x.
If you're are given a function and you want to find the inverse, you can solve for that function in terms of y.
(ie. f(x)=4x-1-->y=4x-1 then you can solve for x in terms of y to find the inverse. So the inverse for f(x) would be f^-1=(y+1)/4 ---> g(x)=(x+1)/4 )
a function is considered one-to-one if there is exactly one output for every input. so if you can take a horizontal line and there are no two points that cross that line, it's one-to-one.
*this is important because the graph of the inverse won't be a function if the original graph is not one-to-one. think of the graph of y=x^2 and it's inverse. it makes a perabola because there's only one y for every x, but the inverse is not a function because there are two y's for every x. \
the book sorta explains it on page 188. i hope this helps.
Well one thing i use for graphing an inverse is rather than switching y and x and then solving for y, i change the calculator into parametric modethen type the equation x=. For example if i wanted to graph the inverse of y=(8x-9)^2, then x=(8t-9)^2, and y=t.
The simplest way to find an invers function is to simply exchange x for y in the equation and solve the new equation for y. You can then check if the equation you found is indeed the inverse function by placing the output of one into the other equation into the inverse and you should get out the prior input.
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