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}

   

Answer 1

(b) {(x, y) : x, y ∈, R, y² = x}

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