SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 1.9Inverse Functions

Homework for section 1.9 P , 31, 33, 43-49, 53, 55, 57, 61, 81, 83, 87-91, 99

A function is a set of ordered pairs:(x,y) (input, output) (domain, range) How would you go backwards? How would you go in the other direction?

Range x yx y DomainRangeDomain Range

By interchanging the x and y coordinates, you can form the inverse function for any function you have … If you know points of a certain function, you can easily create it’s inverse just by switching the x value to the y coordinate, and switching the y value to the x coordinate.. (3,5)(3,5)(5,3)(5,3) (4,8)(4,8)(8,4)(8,4) and so on …

One way to see if things are inverses of each other is to take their composition …

Let’s try a couple … are these inverses? what about these?

Taking the composition was one way of determining if two things are inverses of each other … GRAPHING is another way.

Is the yellow curve a function??? By definition: A function can only have an inverse if the inverse is itself a function … By placing a restriction on a function, you can make it: ONE-TO-ONE

But why stop here?? There is even ONE more way to tell if two things are inverses of each other. (It’s also a way to algebraically PROVE that things are inverses without having to graph.)

Example:

Lets prove it via composition. You will have to know how to do this for the test …

Go! Do!