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f(x) = log((1 + x)/(1 - x)) of a substituted expression in terms of f(x)

The same question, asked 2 times: 4 May 2023 S1*, 25 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S1

    133
    If f(x)=log⁡e ⁣1−x1+x, ∣x∣<1f(x)=\log_e\!\frac{1-x}{1+x},\,|x|<1, then f ⁣(2x1+x2)f\!\left(\frac{2x}{1+x^2}\right) is equal to

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  2. Question 2

    25 Apr 2025 S1

    101
    If f(x)=log⁡(1+x1−x)f(x) = \log\left( \frac{1 +x}{1 -x} \right) and g(x)=3x+x31+3x2g(x) =\frac{3x+x^{3}}{1 + 3x^{2}}, then (fog)(x)=(fog)(x) =

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