Which one of the following is not a function?
Question:
Which one of the following is not a function?
(a) {(x, y) : x, y ∈ R, x2 = y}
(b) {(x, y) : x, y ∈, R, y2 = x}
(c) {(x, y) : x, y ∈ R, x2 = y3}
(d) {(x, y) : x, y ∈, R, y = x3}
Solution:
(b) {(x, y) : x, y ∈, R, y2 = 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.