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Math Help - One-One Functions

  1. #1
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    Smile One-One Functions

    Q.Find the possible domains for which the following are one to one functions

    a) y = x^2

    b) y= x(x-2)

    c) y = 2x-3

    i kno the for a 1-1 function there is max and min of the 1 y-value for every x-value and vice-versa

    all i need is now are the answers and the explanations to the answers.

    for eg i for b) i know that domain: x<=0 or x>=1 but why not x<=0 or x>=2

    i am so damn confused, please help me thank you
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xibeleli View Post
    Q.Find the possible domains for which the following are one to one functions

    a) y = x^2

    b) y= x(x-2)

    c) y = 2x-3

    i kno the for a 1-1 function there is max and min of the 1 y-value for every x-value and vice-versa

    all i need is now are the answers and the explanations to the answers.

    for eg i for b) i know that domain: x<=0 or x>=1 but why not x<=0 or x>=2

    i am so damn confused, please help me thank you
    these are all polynomials. their domain is all real x's, that is, x \in ( - \infty, \infty)


    you probably meant to ask a different question (do you want the domain to be such that the functions are one to one on them?)
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    Quote Originally Posted by Jhevon View Post
    these are all polynomials. their domain is all real x's, that is, x \in ( - \infty, \infty)


    you probably meant to ask a different question (do you want the domain to be such that the functions are one to one on them?)
    no no no u dont get, the questions wants to find the domain to make the equations to be one-one functions
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xibeleli View Post
    no no no u dont get, the questions wants to find the domain to make the equations to be one-one functions
    o ok. obviously, the first is x >= 0 or x =< 0

    the third is one to one on it's original domain

    for the second, look at the graph, now can you see why it is x <= 1 or x >= 1 ?
    Attached Thumbnails Attached Thumbnails One-One Functions-graphquad.jpg  
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    Quote Originally Posted by Jhevon View Post
    o ok. obviously, the first is x >= 0 or x =< 0

    the third is one to one on it's original domain

    for the second, look at the graph, now can you see why it is x <= 1 or x >= 1 ?
    axis of symmetry? kinda get it but still need a little explanation, thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xibeleli View Post
    axis of symmetry? kinda get it but still need a little explanation, thanks
    a one to one function satisfies the horizontal line test. so drawing any horizontal line should cut the graph at only one point. for quadratics, this happens only when our curve does not pass the axis of symmetry, since if it does, it will be increasing on both sides of the axis and a horizontal line will touch it twice
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