Section+1.5

1.5 **Inverse Functions**

REVIEW: __Inverse Operations__ 8 - 5 = **3** <-- undid what the other operation did
 * 3** + 5 = 8

--> __Inverse Relation__
 * the ordered pair (a,b) is in a relation if and only if the ordered pair (b,a) is in the inverse relation.

Ex. f(x)= x²


 * **X** || **Y** ||
 * -2 || 4 ||
 * -1 || 1 ||
 * 0 || 0 ||
 * 1 || 1 ||
 * 2 || 4 ||

To find the graph of the inverse of the function f, switch the domain and range values.


 * **X** || **Y** ||
 * 4 || -2 ||
 * 1 || -1 ||
 * 0 || 0 ||
 * 1 || 1 ||
 * 4 || 2 ||

Graphed together, the function and its inverse look like this:



--> **One-to-One** A function where every y coordinate is paired with a unique x coordinate

If a function is one-to-one, then it has an __inverse function__.

--> **Horizontal Line Test** A function is one-to-one if it passes this test.

For every horizontal line that can be drawn, the graph is only intersected at one point.

--> **Inverse Functions** Plug any number into the domain, and a range value comes out. The hard part comes when you need to find what operation, then, will give you the inverse of that function. If I plug in a 4 and get a 10, what function will allow me to go from 10 back to 4?

__Finding Inverse Functions__ (1) Determine that the function is one-to-one and state the restrictions on the domain (2) Switch x and y (3)Solve for y and state the domain restrictions for the new operation.

__Graphically__ A function and its inverse are symmetric over the line y=x.

--> **Verifying Inverses** you must show that f(g(x)) = g(f(x)) = x.