Please can anyone give some direction.
The function:
g(x)=1/4(x-2)^2-4 (4<x<8)
has the same rule as the function f but has a smaller domain. I have to state the domain and image set of g^-1and find its rule.
Anyone know where I start?
What is "f"? How is it necessary for this exercise?
Your formatting is ambiguous. Do you mean the following?
. . . . .$\displaystyle g(x)\, =\, \frac{1}{4(x\, -\, 2)^2}\, -\, 4\, \mbox{ for }\, 4\, \leq \, x\, \leq \, 8$
The domain of g is given to you in the exercise. The range (the "image set") of g-inverse will be the domain of g, by definition of "inverse". The domain of g-inverse will be the range of g, which you can "see" from the graph of g.
To learn how to find the inverse of a function, try here. If you get stuck, kindly please reply with a clarification of the function g, along with a clear listing of your steps and reasoning so far.
Thank you!