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Monotonicity of log(1 + x) minus a fraction in x

This type of question, asked 2 times: 25 Apr 2025 S2, 17 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    25 Apr 2025 S2

    140
    If f(x)=log⁡(1+x)−2x2+xf(x) = \log(1 +x) -\frac{2x}{2 +x} then f(x)f(x) is increasing in

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  2. Question 2

    17 Apr 2026 S1

    77
    If f(x)=log⁡(1+x)−x1+xf(x) = \log(1 + x) - \dfrac{x}{1 + x}, then the values of xx for which f(x)f(x) is monotonically increasing and monotonically decreasing are respectively.....

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