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Roots of a Quadratic Equation

Which one of ...

Question

Which one of the following is not a function?

A

{(x, y) : x, y ϵ R, x^{2} = y}

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B

{(x, y) : x, y ϵ R, y^{2} = x}

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C

{(x, y) : x, y ϵ R, x^{3} = y}

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D

{(x, y) : x, y ϵ R, y^{3} = x}

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Solution

The correct option is B ${(x, y) : x, y ϵ R, y^{2} = x}$
Let $R_{2} = {(x, y) : x, y ϵ R, y^{2} = x}$
$∴ R_{2}$ is not a function; as y = $\pm$ x.

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Similar questions

Which one of the following is not a function ?

(a) ${(x, y) : x, y ϵ R, x^{2} = y}$
(b) ${(x, y) : x, y ϵ R, y^{2} = x}$
(c) ${(x, y) : x, y ϵ R, x = y^{3}}$
(d) ${(x, y) : x, y ϵ R, y = x^{3}}$

A = {(x, y) : x, y ϵ R, x^{2} + y^{2} = 1},

B = {x : x ϵ N, 2 x^{2} - 1 < 7}

Are A and B comparable ?

Q. 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}

A = {(x, y) : x, y ϵ R, x^{2} y^{2} + y^{2} = 1}

B = {(x, 0) : x ϵ R, - 1 \leq x \leq 1} .

A \cap B = {(- a, 0), (1, b)}

.Find relation between a and b

A = {(x, y) : x^{2} + y^{2} \leq 1; x, y ϵ R}

B = {(x, y) : x^{2} + y^{2} \geq 4; x, y ϵ R}

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Roots of a Quadratic Equation

Standard XII Mathematics

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