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Math Help - Inverse functions.

  1. #1
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    I face another problem childish but still a problem

    Find the inverse functions of

    a) x ---> 2x+3
    b)x---> 3x-4
    c) x---> 2(x+5)
    d) x----> 1 (x-1)
    Last edited by mr fantastic; July 13th 2010 at 05:19 AM. Reason: Moved from another thread
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  2. #2
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    Quote Originally Posted by MrGenuouse View Post
    I face another problem childish but still a problem

    Find the inverse functions of

    a) x ---> 2x+3
    b)x---> 3x-4
    c) x---> 2(x+5)
    d) x----> 1 (x-1)
    I'm going to show you how to get the inverse function with example a). The remaining examples have to be done similarly.

    to #a):

    From f:x\to2x+3 you'll get the equation of the function f:

    f(x)=y=2x+3

    To find the equation of the inverse function you have to swap the variables and solve this equation for y:

    f:y=2x+3~\implies~f^{-1}:x=2y+3

    x=2y+3~\implies~x-3=2y~\implies~\boxed{y=\frac12 x - \frac32}

    (Remark: You'll get the graph of f^{-1} by reflection of the graph of f at the line y = x)

    ... and now it's your turn!
    Last edited by mr fantastic; July 13th 2010 at 05:19 AM.
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  3. #3
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    Another way of thinking about it: f(x)= 2x+ 3 tells you "whatever x is, first multiply by 2, then add 3". To find the inverse of f, do the opposite of each step, in the [b]opposite order. The opposite of "multiply by 2" is "divide by 2" and the opposite of "add 3" is "subtract 3". So the inverse of f is "subtract three, then divide by 2": f^{-1}(x)= \frac{1}{2}(x- 3)= \frac{1}{2}x- \frac{3}{2} just as earboth got.
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