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
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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.