The answer, for y as a function of x, depends on the range of y.
Over the real numbers, it is not a function because a function cannot be one-to-many. But it is always possible to define the domain and range in such a way that the mapping in not one-to-many.
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81 x 81 = 6561
It is: 9^2 = 81
81. 92 = 9 * 9 = 81
Square root of 81 has two solutions: SQRT(81) = +9 and -9 SQRT(81) = +9. The square root function has just a single output for every input. It, by definition, returns the positive 2nd root of the function. So SQRT(x) is always non-negative. This is distinctly different than saying, "what number squared equals 81?" That refers to solutions to the equation x^2 = 81, of which there are two.....+9 and -9.
Because 9 times 9 equals 81.