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Question

Mathematics Question on Relations and functions

Which of the following is not a function?

A

(x,y): x, y ∈R,x2=y\\{(x,y):\,x,\,y\,\in R,{{x}^{2}}=y\\}

B

(x,y): x, y ∈R,y2=x\\{(x,y):\,x,\,y\,\in R,{{y}^{2}}=x\\}

C

(x,y): x, y ∈R,x=y3\\{(x,y):\,x,\,y\,\in R,x={{y}^{3}}\\}

D

(x,y): x, y ∈R,y=x3\\{(x,y):\,x,\,y\,\in R,y={{x}^{3}}\\}

Answer

(x,y): x, y ∈R,y2=x\\{(x,y):\,x,\,y\,\in R,{{y}^{2}}=x\\}

Explanation

Solution

∵\because y2=x     ⇒     y=±x{{y}^{2}}=x\,\,\,\,\,\Rightarrow \,\,\,\,\,y=\pm \sqrt{x}
is one value of x gives two values of y. So,
(x,y): x,∈R, y2=x\\{(x,y):\,x,\in R,\,{{y}^{2}}=x\\} is not a function.