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Math Help - Bijections

  1. #1
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    Bijections

    how do you tell if a function is a bijection? can someone please give me an example?
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  2. #2
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     f: \mathbb{R} \to \mathbb{R} defined by  f(x) = x . Show that it is injective and surjective.
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    sorry i mean like when you are given the function like 3x-2 and you need to see if it is a bijection? i know the definitions that i needs to be one to one and onto. i am just wondering how do you tell this from the function? do you graph it or i mean i dunno im so confused!
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    Quote Originally Posted by srw899 View Post
    sorry i mean like when you are given the function like 3x-2 and you need to see if it is a bijection? i know the definitions that i needs to be one to one and onto. i am just wondering how do you tell this from the function? do you graph it or i mean i dunno im so confused!

    You can tell by the graph. It passes the horizontal line test.
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  5. #5
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    im sorry but i forget, how do you do the horozontal line test? (*im sorry if i seem dumb, and thank you so much for your help, i really appreciate it*)
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  6. #6
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    alright ive got it, thanks so much!!! wow i feel befuddled! for others:

    horozontal line test is when you graph the function and draw a horozontal line, if it crosses the function more than once then once the function is not one to one.
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  7. #7
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    bijections are true both ways.

    if a bijection is true, then the converse of the bijection is true.
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    other than graphically, you can show a function is a bijection if it is one-to-one and onto, that is, it is both injective and surjective. a quick wiki or google search can show you what these are
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