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Question
Which one of the following is not a function?
Options
(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}
\[y^2 = x \text{ gives two values of y for a value of x }. \]
\[i . e .\text{ there are two images for a value of x } . \]
\[\text{ For example: } (2 )^2 = 4 \text{ and } ( - 2 )^2 = 4\]
\[\text{ Thus, it is not a function . } \]
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