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Functional equation in f(x) and f(1/x): solve for f, then differentiate

This type of question, asked 2 times: 4 May 2023 S1, 19 May 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    4 May 2023 S1

    105
    If 8f(x)+6f ⁣(1x)=x+58f(x)+6f\!\left(\frac{1}{x}\right)=x+5 and y=x2f(x)y=x^2 f(x), then dydx\frac{dy}{dx} at x=−1x=-1 is

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  2. Question 2

    19 May 2026 S1

    72
    Let 3f(x)−2f(1x)=x3f(x) - 2f\left(\dfrac{1}{x}\right) = x for x≠0x \neq 0. Then the value of f′(2)f'(2) is:

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