Pre-Cal 40s: Inverse Function

Hello everyone in Mr.Piatek's pre-cal class. my name is Robbie, but most of you probably know me as the class genius, always helping out Mac and Justin with their homework.

 Isn't this a lovely Friday we are having? And what better way to start off the month and end the school week than to have not one, but two periods of pre-cal!!!!!! Gosh, we are just so lucky!!

 Anyways, I decided that for my blog entry, instead of trying to fill up as much space as I can with a whole bunch of information that the majority of you will never read, I will dedicate this post to one specific topic. I'm also doing this partially because it's a little after midnight and I just got home from curling and really don't want to spend 2 hours typing this out.

So here it goes...

Inverse of a relation:

* When X is interchanged with Y in the equation of a function y=f(x) , it's reflected in the mirror line y=x. This is called an inverse function.*

So how do you find the inverse of a function? Well there are four steps that you must follow in order to do so.

The steps are: 1) replace f(x) with y

                      2) switch x and y

                      3) solve for y

                      4) replace y with Fin(x)

Example:   

               f(x)=2x+2

               y=2x+2

               x=2y+2

               x-2=2y

               x-2/2=y

               y=x-2/2

               y=1/2x-1

               Fin(x)=1/2x-1

Once you have done this, you can graph the new function.

Another way to graph the inverse of a function is to reflect the X,Y points on the opposite side of the mirror line.(the mirror line equates to y=x). We do this by simply switching the X and Y values.

Example:   (2,6) ---> (6,2)

                 (1,4)---> (4,1)

                 (0,2)---> (2,0)

Here are some pictures of inverse functions that will hopefully give you a better understanding of the topic. If you still need help, Khan Academy has some great video's on the subject, but I'm way too tired to go to all of the trouble of uploading them tonight.

 

I hope you all enjoyed reading my blog and found it useful. Have a good weekend!!

Oh, and Mr.P, I don't need to pick a number to see who will write the next blog entry. I know exactly who I want... Can't wait to read your blog Justin!!!