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It depends on the domain of y. If that is restricted to non-negative values, then the answer is yes. But if y is allowed to be negative, then the answer is no because then there are two values of y for each non-zero value of x.
The property of the reciprocal of the opposite of a number is: Reciprocals of inverse values are themselves inverse values. i.e. for b = (-1)a , the reciprocal 1/b = (-1) 1/a The negative or positive status of a reciprocal is the same as that of the original number.
The plus values become negative and the negative values become positive although their numerical values remain the same
Yes
Yes.