Question

Which of the following is not a function?

• A. $ \{(x,y):\,x,\,y\,\in R,{{x}^{2}}=y\} $
• B. $ \{(x,y):\,x,\,y\,\in R,{{y}^{2}}=x\} $
• C. $ \{(x,y):\,x,\,y\,\in R,x={{y}^{3}}\} $
• D. $ \{(x,y):\,x,\,y\,\in R,y={{x}^{3}}\} $

Answer 1

Answer: (B)

$ \because $ $ {{y}^{2}}=x\,\,\,\,\,\Rightarrow \,\,\,\,\,y=\pm \sqrt{x} $
is one value of x gives two values of y. So,
$ \{(x,y):\,x,\in R,\,{{y}^{2}}=x\} $
is not a function.