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Why do interests rates on loans to be lower in a weak economy than in a strong one

If g^-1(x) is the inverse of g (x) which statement must be true

Three numbers x, y, and z are in the ratio 2: 7: 8. if 12 is subtracted from y, then three numbers form a geometric sequence (in the order x, y–12, z). find x, y, and z. there are 2 sets.