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Math Help - function question

  1. #1
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    function question

    Let R be the set of real numbers.let A=R - {-1/2} and B=R - {2}.let f be a function from A to B defined by f(x)= 4x-3 / 2x+1.

    i) Show that f is 1-1
    ii) show that f is onto
    iii) does f have an inverse? if so find the inverse?


    i)f(a)= 4a-3 / 2a+1

    f(b) = 4b-3 / 2b+1

    4a-3 / 2a+1 = 4b-3 / 2b+1
    4a-3(2b+1) = 4b-3(2a+1)
    8ab-6b+4a-3 = 8ab-6a+4b-3
    -6b = -6a
    a=b
    hence 1-1

    Im having trouble with the onto and inverse part. Can someone assist me please?
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  2. #2
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    Re: function question

    To get the inverse let f(x)=y
    y= \frac{4x-3}{2x+1}

    Rearrange this to get x in terms of y
    Then change the variables so that x becomes f(x) and y becomes x
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  3. #3
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    Re: function question

    For a function to be invert-able it must be 1-1 and onto .I got that part but how do i do the inverse?
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  4. #4
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    Re: function question

    I just explained how to get the inverse. Try it and if it doesn't work then show us what you tried
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  5. #5
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    Re: function question

    Quote Originally Posted by Shakarri View Post
    I just explained how to get the inverse. Try it and if it doesn't work then show us what you tried
    x= y-3 / 2y - 4

    f(x) = x-3 / 2x - 4

    is this it?
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