Which of the following are functions?

Question:

Which of the following are functions?

(a) {(xy) : y2 = xxy ∈ R}

(b) {(xy) : y = |x|, xy ∈ R}

(c) {(xy) : x2 + y2 = 1, xy ∈ R}

(d) {(xy) : x2 − y2 = 1, xy ∈ R}

Solution:

(b) {(xy) : y = |x|, xy ∈ R}

For every value of ∈ R, there is a unique value y∈ R.

i.e. there is a unique image for all values of ∈ R.

Also, values of x occur only once in the ordered pairs.

Thus, it is a function.

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