to find the inverse of G(x)
let y = 1/3(x-2)^2 - 3
to take the inverse...
Step 1, interchange the x and y variables
Step 2, solve this for y
---> x = 1/3(y-2^2 - 3
3x = (y-2)^2 - 9
(y-2)^2 = 3x+9
y-2 = ±√(3x+9)
y = 2 ± √(3x+9)
so g^-1(x) = 2 ± √(3x+9)
I am not quite sure what you mean by y=g^-x
I think my reply also ties in with your other post,
re domain and range
the domain of a function becomes the range of its inverse, and vice versa
so find g(2) and g(5) for the first function and those values would then be the domain of your inverse
given function G(x)=1/3(x-2)^2-3 2<x<5 sketch a graph of function y=g^-x and find the inverse function g^-1
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