inverse functions

**redieeee_babieeee** · November 17th 2008, 02:54 AM

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

**Soroban** · November 17th 2008, 06:30 AM

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).

**redieeee_babieeee** · November 17th 2008, 11:30 AM

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!!

**mr fantastic** · November 17th 2008, 11:34 AM

Originally Posted by redieeee_babieeee

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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