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For the function f(x) = log(x + √(x² + 1)), which of the following describes it correctly?

1. It is neither even nor odd
2. It is an even function
3. It is an odd function
4. It is a periodic function

Correct answer: It is an odd function

Solution

f(-x) = log(-x + sqrt(x^2+1)) = log(1/(x + sqrt(x^2+1))) = -log(x + sqrt(x^2+1)) = -f(x). Since f(-x) = -f(x), the function is odd.

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