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Inverse functions: Logarithms and Exponentials Fr. Chris’ Chapter 6 Overview

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How long for how many? To make one photocopy takes 6 seconds To make 10 copies takes 15 seconds 30 copies takes how long? How many copies can be made in 1 minute?

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Notice how if you do both functions, you end up where you began In general

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Not all have inverses “Horizontal Line Test” Functions must be “one-to-one” to have an inverse function

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6.1(403)#50

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Check (using algebra)

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Check(using graphic calc) Is it symmetric around the diagonal identity line? (Try 5.ZoomSquare)

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Now try this one... What is the inverse of this?????

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www.mathorama.com/hatt/exponential.html

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In general... “What power of b gives me A?” is written: so if then

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6.2(414)#36

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6.2(414)#44

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What is e??????? See page 410 or Mathematica Can you find e on your calculator?

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6.2(414)#48 remember how So both x=6 and x=-2 work!

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6.2(415)#61

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6.3 (425)#2, #6 and #10

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6.3(426) #26 (no calc) So... To check with your calc:

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The graph of log

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Horizontal Shift

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6.3(p426) #54 Right shift by 1...

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3.3 Logarithmic Functions and Their Graphs

3.3 Logarithmic Functions and Their Graphs

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