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Which of the following defines an implicit function?

1. x*y - sin(x + y) = 0
2. y = (x² + e^x + 5)/sqrt(1 - arccos(x))
3. y = x²
4. y = x²*log(x)/sin(x)

Correct answer: x*y - sin(x + y) = 0

Solution

In x*y - sin(x + y) = 0, y cannot be solved for explicitly in terms of x — it is defined implicitly. The other three are written as y = f(x) explicitly.

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