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Composite of two given functions as an expression in x

This type of question, asked 3 times: 4 May 2023 S2, 11 May 2024 S2, 17 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    134
    If f(x)=x2−xf(x)=\dfrac{x}{2-x}, g(x)=x+1x+2g(x)=\dfrac{x+1}{x+2}, then (g∘g∘f)(x)=(g\circ g\circ f)(x)=

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  2. Question 2

    11 May 2024 S2

    128
    If f(x)=3x+45x−7f(x)=\frac{3x+4}{5x-7} and g(x)=7x+45x−3g(x)=\frac{7x+4}{5x-3}, then f(g(x))=f(g(x))=

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  3. Question 3

    17 Apr 2026 S2

    67
    If f(x)=1−x1+xf(x) = \dfrac{1 - x}{1 + x}, then f(f(cos⁡x))=f(f(\cos x)) =

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