If G^ -1(y) is the inverse of G(x), which statements must be true?
A. The domain of G -1(y) is the domain of G(x).
B. G -1(G(x)) = x
C. The range of G -1(y) is the range of G(x).
D. G(G -1(x)) = x
E. The domain of G -1(y) is the range of G(x).
F. The range of G -1(y) is the domain of G(x).

Question

If G^ -1(y) is the inverse of G(x), which statements must be true?
                A.	The domain of G -1(y) is the domain of G(x).
 		B.	G -1(G(x)) = x
 		C.	The range of G -1(y) is the range of G(x).
 		D.	G(G -1(x)) = x
 		E.	The domain of G -1(y) is the range of G(x).
 		F.	The range of G -1(y) is the domain of G(x).

freckles · Answer

Example:
Let f(x)=sqrt(x-1) (this has domain [1,inf) and range [0,inf)
Then g(x)=x^2+1 is its inverse if we restrict its domain to [0,inf) and its range to [1,inf)

Recall f is a reflection of g about the y=x line
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Anyways
what happens when you simplify f(g(x)) and g(f(x))