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If f(x) = logₑ((1 - x)/(1 + x)), |x| < 1, then f(2x/(1 + x²)) is equal to -

1. 2f(x)
2. 2f(x²)
3. (f(x))²
4. -2f(x)

Correct answer: 2f(x)

Solution

The function f(x) is defined in terms of a logarithmic expression, and substituting 2x/(1 + x²) into f results in a transformation that effectively doubles the input value of f(x), leading to the conclusion that f(2x/(1 + x²)) equals 2f(x).

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