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Which of the following defines y as an implicit function of x?

1. xy - cos(x + y) = 0
2. y = x³
3. y = log(x² + x + 1)
4. y = |x|

Correct answer: xy - cos(x + y) = 0

Solution

An explicit function expresses y directly in terms of x (y = f(x)). Options y = x³, y = log(x² + x + 1), and y = |x| are all explicit. The relation xy - cos(x + y) = 0 mixes x and y and cannot be solved in closed form for y, so it is an implicit function.

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