Question

Which one of the following is not a function ?

(a) $\left\{\right(x,y):x,yϵR,x^2=y\}$
(b) $\left\{\right(x,y):x,yϵR,y^2=x\}$
(c) $\left\{\right(x,y):x,yϵR,x=y^3\}$
(d) $\left\{\right(x,y):x,yϵR,y=x^3\}$

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

Answer 1

The correct option is B

$\left\{\right(x,y):x,yϵR,y^2=x\}$

$(x,y):x,yϵR,y^2=x$
$y^2=x$ 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.