SOLUTION: Is {(x, y)| y^4 = x − 3} a function?

Algebra ->  Functions -> SOLUTION: Is {(x, y)| y^4 = x − 3} a function?      Log On


   

Question 1188640: Is {(x, y)| y^4 = x − 3} a function?
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

The answer is   highlight%28No%29. 

                        EXPLANATION


For example, for x = 4, we have two values y= 1 and y= -1 both satisfying the equation.


But, according to definition of function, the value, corresponding to x= 4 should be UNIQUE.

Solved and thoroughly explained.


/////////////


By the way,  the given  relation  determines  x  as a function of  y.


But this relation does not determine  y  as a function of  x.


So,  be alert  ( ! )


\\\\\\\\\\\\\


Strictly speaking,  your problem/question is defective :   it asks if the relation determines a function,

but does not tell  WHICH  function :   y = y(x)   or   x = x(y).


So,  be alert  TWICE  ( ! )