Lesson 8.2: Inverses of Relations
3 Important things to know about inverses of relations:
Suppose f is a relation and g is the inverse of f;
1) A rule (or equation) can be found by switching x and y (solving for y if necessary)
2) A graph for g is found by reflecting f over y=x,
3) The domain of g is the range of f, and the range of g is the domain of f
An example of inverse relation is this;
Let f = (1,4) (2,8) (3,8) (0,0) (-1,-4)
The inverse relation of this would be;
(4,1) (8,2) (8,3) (0,0) (-4,-1)
Another thing to note, is that the f is a function but the inverse of f is not.
This is because when you reverse x and y, there becomes (8,2) and (8,3) which means it is not a function.
You can also find out if the inverse is a function by seeing if it passes the horizontal line test.
The domain of f is ( 1, 2, 3, 0, -1) and the range is ( 4, 8, 0, -4)
The domain of the inverse is (4, 8, 0, -4) and the range is (1, 2, 3, 0, -1)
You should note that the domain and range swap when it is the inverse.
Another example is f 9x0 = 1/2x + 4
The work I did to find the inverse is;
I rewrote the equation to be y = 1/2x + 4
Then rewrote it as x = 1/2y + 4
Then I subtracted the 4
So its now x - 4 = 1/2y
Then I multiplied both sides by 2 to get ride of the fraction
So it would now be 2x-8 = y which is the final answer.
I hope this helps!
802 and the 3 problems on the back of the worksheet.
The next scribe will be Leah.