Which One of the Following is Not a Function?
Question:
Which one of the following is not a function?
(a) \( \{(x,y): x^2=y\} \)
(b) \( \{(x,y): y^2=x\} \)
(c) \( \{(x,y): x=y^3\} \)
(d) \( \{(x,y): y=x^3\} \)
Solution:
A relation is a function if each value of \(x\) has exactly one value of \(y\).
In option (b),
\[ y^2=x \]
\[ y=\pm \sqrt{x} \]
One value of \(x\) gives two values of \(y\).
Therefore, it is not a function.
\[ \boxed{\text{Correct Answer: (b)}} \]