If G -1(x) is the inverse of G(x), which statements must be true?

Check all that apply.

A. The domain of G -1(x) is the domain of G(x).
B. The domain of G -1(x) is the range of G(x).
C. The range of G -1(x) is the domain of G(x).
D. The range of G -1(x) is the range of G(x).
E. G -1(G(x)) = x
F. G(G -1(x)) = x

Question

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

anonymous · Answer

A - FALSE, because with inverses, the domain of one is the range of it's inverse, and vice-versa.

B - TRUE, using the same logic as in the first statement.

C - TRUE, using the same logic as in the first statement.

D - FALSE, using the same logic as in the first statement.

E - TRUE, if there was a point on G(x) such that (1,2), then there would be a point on G^-1(x) such that (2,1). So, if you use x=1, then G(1) would be 2, and G^-1(2) would be 1, which is x.

F - TRUE, on the same principle as E.