Inverse Functions

If you have a relation with ordered pairs and certain coordinates, the inverse of this would be the reflection of the y=x line.

(-3,2)(1,4)(5,7)(6,8)

Inverse: (2,-3)(4,1)(7,5)(8,6)

The x and y coordinates are just reversed.

Here are the steps to finding the inverse function with a relation.

Relation: f(x) = 2x - 1

1. Replace f(x) with y.

y = 2x -1

2. Switch x and y.

x = 2y - 1

3. Solve for y.

4. Replace y with

Here are both the original and inverse relations graphed. Notice how each line is a reflection of one another of the y=x line.

The coordinates (-1,0) are the original relation, while (0,-1) are the inverse.

This is how to determine whether 2 functions are inverses of each other.

f(x) = 2x - 7, g(x) = 7x + 2

You will need to plug in g(x) into f(x)

f(g(x)) = 2(7x + 2) - 7

= 14x + 4 - 7

= 14x - 3

Now, you will need to plug in f(x) into g(x)

g(f(x)) = 7(2x - 7) + 2

= 14x - 49 + 2

= 14x - 47

f(x) and g(x) are not inverses of each other because f(x) does not equal x, nor does g(x).

HURRAY GUUIISE!

I'm pretty sure everybody understood what was going on in class today. :D

Only a few more weeks of school left! Who's excited for summer break?!