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For the function f(x) = ln((x² + e)/(x² + 1)), what is the set of all possible values of f(x)?

1. (0, 1)
2. (0, 1]
3. [0, 1)
4. (0, 1]

Correct answer: (0, 1]

Solution

The function f(x) is the natural logarithm of a fraction that approaches 1 as x approaches infinity, resulting in f(x) approaching 0, but never reaching it. The logarithm of 1 is 0, and since the fraction is always greater than 1 for all x, the function can take values just above 0 up to and including 1.

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