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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}

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Solution

## (b) {(x, y) : x, y ∈, R, y2 = x} ${y}^{2}=x\mathrm{gives}\mathrm{two}\mathrm{values}\mathrm{of}y\mathrm{for}\mathrm{a}\mathrm{value}\mathrm{of}x.\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.\mathrm{there}\mathrm{are}\mathrm{two}\mathrm{images}\mathrm{for}\mathrm{a}\mathrm{value}\mathrm{of}x.\phantom{\rule{0ex}{0ex}}\mathrm{For}\text{example:}\left(2{\right)}^{2}=4\mathrm{and}\left(-2{\right)}^{2}=4\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{it}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{function}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

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