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Question

Which one of the following is not a function ?

(a) {(x,y):x,yϵR,x2=y}
(b) {(x,y):x,yϵR,y2=x}
(c) {(x,y):x,yϵR,x=y3}
(d) {(x,y):x,yϵR,y=x3}



A

{(x,y):x,yϵR,x2=y}

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B

{(x,y):x,yϵR,y2=x}

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C

{(x,y):x,yϵR,x=y3}

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D

{(x,y):x,yϵR,y=x3}

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Solution

The correct option is B

{(x,y):x,yϵR,y2=x}


(x,y):x,yϵR,y2=x
y2=x gives two values of y for a value of x. i.e. there are two images for a value of x.
For example : (2)2=4 and (2)2=4. Thus, it is not a function.


Mathematics
RD Sharma
Standard XI

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