If f(x) = log((1 + x)/(1 − x)), −1 < x < 1, then f(2x/(1 + x²)) is equal to:
If f(x) = log((1 + x)/(1 − x)), −1 < x < 1, then f(2x/(1 + x²)) is equal to:
- A. 2f(x)
- B. (f(x))²
- C. f(x)/2
- D. 2 f(x²)
Answer: A) 2f(x)
Explanation: f(x) = log(1+x) − log(1−x). Then f(2x/(1+x²)) = log(1 + 2x/(1+x²)) − log(1 − 2x/(1+x²)) = log((1+x)²/(1+x²)) − log((1−x)²/(1+x²)) = 2 log(1+x) − 2 log(1−x) = 2f(x).
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