The Inverse of a Relation

Hey guys this is Mathew Dunning, I sit near the back of the class room in the corner. If you don't know which one I am, you can probably look up considering I am pretty tall, but enough about me lets start talking precal.

So first I will show you how to find the Inverse of a Relation.  To find the Inverse of a Relation and graph you switch the X and Y axis.  The steps to find an Inverse of a function are:

1) Replace f(x) with y

2) Switch x and y

3) Solve for y

4) Replace y with f-1(x)

For Example:  f(x)= 2x+2

y=2x+2

x=2y+2

x-2=2y

y=x-2

    ----

      2

y= 1

    ---- x-1

      2

f-1(x)=1

          ---- x-1

            2

Also in class we worked on finding the domain and range!

This is how you find the domain and range,

Domain is left to right on the graph so if you look at Example #1 in your booklets you can see that the farthest point to the left on the x axis is -5, and the farthest point to the right on the x axis is +4 so then the domain of that function would be (-5,4)

The range is almost the same thing but it goes from low to high so if you look at the original graph you can see the lowest point on the y axis is 1, and the highest point on the y axis is 5 so then we know that the graphs range is (1,5)

If we wanted to find the inverse of the domain and range we would simply switch x and y so then the domain would switch with the range. So the inverse domain would be (1,5) and the inverse range would be (-5,4).

Next we had some examples about applying reflections & inverse.

I will show you a few examples of how to do them. For all your questions the coordinates are (1, -1/2).

ex A. -f(x)

Since the f is negative you know that there will be a reflection in the x axis and you make all y values negative. So then -f(x)= (1,1/2)

ex B. f(-x)

Since the x is negative we know that the reflection will be in the y axis, and you make all x values negative. So then f(-x)= (-1,-1/2)

If you look at the graph on Example #2 you can see how -f(x) makes all the y values negative.

the coordinates change to:

(-4,0) -- (-4,0)

(-2,-1) -- (-2,1)

(-1,2) -- (-1,-2)

(1,4) -- (1,-4)

(2,0) -- (2,0)

Then you just graph the new points and connect the dots!

If you look at Example 5, this is where Mr.P played a trick on us and the questions asks if the two different graphs are inverses of one another.  If you coordinate the points without looking at the different graphs your answer would be yes! but he told us since the lines do not connect the same way they would not be considered inverses of eachother. So don't always let the coordinates trick you sometimes just by looking you can use common sense and tell what the answer will be.

Well guys that is all for now , I will see you tomorrow and I hope everyone had a good time at TA day! :)