Although we cant do that in our own lives in the

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something we’d like to have back. Although we can’t do that in our own lives, in the world of functions, this is sometimes possible. Let me show you. Example 5 I’m thinking of an integer between 4.5 and 5.5, and I’m selfish. I’m not going to tell you what it is. If you tell me to take my number and add three to it, then quadruple it, then subtract 4, then divide by two, I would give you THAT number. Assuming I did, how could you find my original number about which I was so secretive, guarded, and selfish? Was that last example Magic? Mathmagic? Cheesy? The point is, there was a process for working backwards from the original output to arrive at the original input, and this input was unique. This is because the function I used to “scramble” my number was one-to-one , making my cipher “invertible.” When a function is inverted, all the x and y information interchange. Consequently, an invertible function containing the point ( , ) a b means that its inverse will contain the point ( , ) b a . This has several implications, besides 1 ( ) ( ) f a b f b a ³ . If ( ) y g x is 1:1 over a domain, To graphically find the graph of 1 f ³ , reflect the graph of f over the line y = x.
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  • Fall '19
  • Inverse function, Injective function

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