SOLUTION: State with a cogent reason whether or not the relationship: y=√x³ represents y as a function of x for both variables coming from the real number system

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Question 1206522: State with a cogent reason whether or not the relationship: y=√x³ represents y as a function of x for both variables coming from the real number system
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Since each real number x has exactly one real cube root, that proves
y=root%283%2Cx%29 represents y as a function of x.

Cubing both sides gives the equivalent equation: y%5E3=x or x=y%5E3
Since each real number y has exactly one real cube, that proves x=y%5E3
represents x as a function of y.

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The statement of the problem does not use good mathematical language....

My guess as to the meaning of "... for both variables coming from the real number system" is that the set of all real numbers is both the domain and range of the function.

In that case, the relation y=sqrt%28x%5E3%29 does not satisfy that condition, because y is not real when x is negative.