inversefunctions

inversefunctions - n the last example from the previous...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
n the last example from the previous section we looked at the two functions and and saw that and as noted in that section this means that there is a nice relationship between these two functions. Let’s see just what that relationship is. Consider the following evaluations. In the first case we plugged into and got a value of -5. We then turned around and plugged into and got a value of -1, the number that we started off with.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
In the second case we did something similar. Here we plugged into and got a value of , we turned around and plugged this into and got a value of 2, which is again the number that we started with. Note that we really are doing some function composition here. The first case is really, and the second case is really, Note as well that these both agree with the formula for the compositions that we found in the previous section. We get back out of the function evaluation the number that we originally plugged into the composition. So, just what is going on here? In some way we can think of these two functions as undoing what the other did to a number. In the first case we plugged into and then plugged the result from this function evaluation back into and in some way undid what had done to and gave us back the original x that we started with. Function pairs that exhibit this behavior are called inverse functions . Before formally defining inverse functions and the notation that we’re going to use for them we need to get a definition out of the way. A function is called one-to-one if no two values of x produce the same y . Mathematically this is the same as saying,
Background image of page 2
So, a function is one-to-one if whenever we plug different values into the function we get different function values. Sometimes it is easier to understand this definition if we see a function that isn’t one-
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 11

inversefunctions - n the last example from the previous...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online