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Math Help - inverse functions

  1. #1
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    inverse functions

    hi! i have to write down the domain, image set of g^-1(inverse function and find it's rule

    g(x)=1/4(x+2)^2 - 4 (0<_ x<_ 4)

    (<_ is the only way i know to write more than or equal to or less than n equal to)

    i have already drawen a graph for G(x)= 1/4 (x+2) ^2 - 4 but then without an image set would the graph of the reverse be the same shape but flipped in the 45dergree angle ??

    please trt n break it down i dont just want the anwser i really wanna be able to understand how to do this in the future

    thanx xx
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  2. #2
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    Hello, redieeee_babieeee!

    I can graph the function for you . . .


    Find the domain, image set of g^{-1} and find its rule.

    . . g(x)\:=\;\tfrac{1}{4}(x+2)^2-4,\quad 0 \leq x \leq 4

    g(x) is an up-opening parabola, vertex (-2,-4).
    x-intercepts: 2, -6. .y-intercept: -3
    Code:
                         |
      o           :      |    * (4,5)
                  :      |
                  :      |
       o          :      |   *
                  :      |
    - - o - - - - + - - -+- * - - -
      -6 o        :      | * 2
           o      :      *
              o   :   o  |-3
                - o      |
               (-2,-4)   |

    The graph runs from (0,-3) to (4,5).

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  3. #3
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    i still need to find out the g^-1

    hiya thanx for the graph its great looks exactly how i did it but now i know the range i do still need to find out how to specify the doman abd the range as well as draw the graph y=g^-1(x) dunno if anyone can help!!
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  4. #4
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    Quote Originally Posted by redieeee_babieeee View Post
    hiya thanx for the graph its great looks exactly how i did it but now i know the range i do still need to find out how to specify the doman abd the range as well as draw the graph y=g^-1(x) dunno if anyone can help!!
    It's expected that you know that \text{dom} \, g^{-1} = \text{ran} \, g and \text{ran}\, g^{-1} = \text{dom} \, g and you should know how to get \text{ran} \, g and \text{dom} \, g.
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