Which of the following are functions-a x- y- y2-x- x- y - R b x- y- y-x- x- y - R c x- y- x2-y2-1- x- y - R d x- y- x2-y2-1- x- y - R

(b) (x, y) : y = |x|, x, y isin; R For every value of x isin; R, there is a unique value y isin; R. i.e. there is a unique image for all values of x ...

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Standard XII

Mathematics

Statement

Which of the ...

Question

Which of the following are functions?

(a) {(x, y) : y² = x, x, y ∈ R}
(b) {(x, y) : y = |x|, x, y ∈ R}
(c) {(x, y) : x² + y² = 1, x, y ∈ R}
(d) {(x, y) : x² − y² = 1, x, y ∈ R}

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Solution

(b) {(x, y) : y = |x|, x, y ∈ R}

For every value of x ∈ R, there is a unique value y∈ R.
i.e. there is a unique image for all values of x ∈ R.
Also, values of x occur only once in the ordered pairs.
Thus, it is a function.

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Which of the following are functions? (a) {(x, y) : y2 = x, x, y ∈ R} (b) {(x, y) : y = |x|, x, y ∈ R} (c) {(x, y) : x2 + y2 = 1, x, y ∈ R} (d) {(x, y) : x2 − y2 = 1, x, y ∈ R}

(b) {(x, y) : y = |x|, x, y ∈ R} For every value of x ∈ R, there is a unique value y∈ R. i.e. there is a unique image for all values of x ∈ R. Also, values of x occur only once in the ordered pairs. Thus, it is a function.

Which of the following are functions?

(a) {(x, y) : y² = x, x, y ∈ R}
(b) {(x, y) : y = |x|, x, y ∈ R}
(c) {(x, y) : x² + y² = 1, x, y ∈ R}
(d) {(x, y) : x² − y² = 1, x, y ∈ R}

(b) {(x, y) : y = |x|, x, y ∈ R}

For every value of x ∈ R, there is a unique value y∈ R.
i.e. there is a unique image for all values of x ∈ R.
Also, values of x occur only once in the ordered pairs.
Thus, it is a function.