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 + 4The 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!

Homework :

802 and the 3 problems on the back of the worksheet.

The next scribe will be Leah.

## No comments:

## Post a Comment

Note: Only a member of this blog may post a comment.