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

Algebra.Com
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)   (Show Source): You can put this solution on YOUR website!
Since each real number x has exactly one real cube root, that proves
 represents y as a function of x.

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

Edwin
Answer by greenestamps(13200)   (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 does not satisfy that condition, because y is not real when x is negative.
RELATED QUESTIONS

Determine whether or not the equation represents y as a function of x.... (answered by solver91311)
Determine whether or not the equation represents y as a function of x. Please show work. (answered by ikleyn)
Determine whether or not the equation represents y as a function of x. Please show work. (answered by ikleyn)
State whether the relationship between the variables in the table is a direct variation,... (answered by sachi)
State whether or not the given equations determines y as a function of x 1. X+Y=1 2.... (answered by MathLover1,ikleyn)
Determine whether or not the equation represents y as function of x? Explain your... (answered by josgarithmetic)
Determine whether the equation represents y as a function of x.... (answered by KMST)
Which of the following best describes the difference between the interpretation of the... (answered by robertb)
Determine whether the equation represents y as a function of x.... (answered by foxxtriton09)