Graphing Inverse Functions

Last Lesson, we learned about inverse functions. By now, you should have a basic idea of what an inverse function is and how to solve an inverse function. Today, we're going to go deeper. We're going to try to map out an inverse function on a graph!

To make the most out of the lesson, please make sure you are comfortable with interpreting and plotting simple linear graphs.

Alright.
 Look at this graph...or graphs

Pay attention to the blue line. Ok. Now, lets work out the inverse of the blue function f(x)=2x+1...If you do not know how to do this, go back to the last tutorial and LEARN !!! You're going to be seriously confused if you don't read that post! Alright...Enough ranting, lets solve.

Use the algorithm I told you guys about in the previous post.

1. f(x)=2x+1

2. y=2x+1

3. x=2y+1

4.  2y=x-1
   y=(x-1)/2 (Divide each side by 2 to make 'y ' the subject)

5. f^-1(x)=(x-1)/2

Now, are answer is in fact, the red line! If you plot them onto a graph, you get two linear equations, and yea, I think the graph gives it away, the inverse is basically a reflection in the equation y=x !!!

So, next time you plot a graph....if you want to map the inverse on a graph, simply draw the line y=x (shown above), and reflect all your points in the original function in the line y=x to get the graph of the inverse!.


Magic.