RedAssign2[1].3 - Do not confuse this with an exponent of...

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Unit: Elementary Functions and Their Inverses Module: Inverse Functions The Basics of Inverse Functions [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1559 –rev 06/13/2001 Inverse functions undo each other. In inverse functions, the dependent variable and independent variable switch roles. The graph of an inverse function looks like a mirror reflection of the original graph. Functions that are not one-to-one do not have inverses. One-to-one functions pass both the vertical line test and the horizontal line test . A function f is like a machine which takes a number x and cranks out another number, f ( x ). It can be helpful to have a machine that reverses the process of the first machine. That machine is called the inverse function of the original function. The inverse of a function f is noted by a raised –1.
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Unformatted text preview: Do not confuse this with an exponent of –1, which symbolizes the reciprocal. If you have a function that relates two variables, x and y , then the inverse function will switch them. You can make the switch graphically by reflecting the first graph across the line given by y = x . You can verify algebraically that f and − 1 f are inverses of each other by composing them. Both f –1 ( f ( x ) ) and f ( f –1 ( x ) ) should equal x . If the reflected image of a function does not pass the vertical line test , then it is not a function. Therefore the inverse does not exist. You can see that if the curve of the original function (on the left) does not pass the horizontal line test , then its reflection (on the right) will not pass the vertical line test. If a function is strictly increasing or strictly decreasing, then it is one-to-one ....
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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