`-2f(x)+1/2 f(1/x)=1-3x` `( ∀x)` Tìm `f(-3)`

Question

`-2f(x)+1/2 f(1/x)=1-3x` `( ∀x)`
Tìm `f(-3)`

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Alexandra 4 ngày 2021-12-06T14:32:53+00:00 1 Answers 4 views 0

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    2021-12-06T14:34:19+00:00

    Đáp án: $f\left(-3\right)=-\dfrac{28}5$

    Giải thích các bước giải:

    Với $x=-3$
    $\to -2f\left(-3\right)+\dfrac12f\left(\dfrac{1}{-3}\right)=1-3\cdot \left(-3\right)$
    $\to -2f\left(-3\right)+\dfrac12f\left(-\dfrac13\right)=10$
    $\to \dfrac12f\left(-\dfrac13\right)=10+2f\left(-3\right)$
    $\to f\left(-\dfrac13\right)=20+4f\left(-3\right)$
    $\to -2f\left(-\dfrac13\right)=-40-8f\left(-3\right)$
    Với $x=-\dfrac13$
    $\to -2f\left(-\dfrac13\right)+\dfrac12f\left(\dfrac1{-\dfrac13}\right)=1-3\cdot \left(-\dfrac13\right)$
    $\to -2f\left(-\dfrac13\right)+\dfrac12f\left(-3\right)=2$
    $\to -40-8f\left(-3\right)+\dfrac12f\left(-3\right)=2$
    $\to -\dfrac{15}2f\left(-3\right)-40=2$
    $\to -\dfrac{15}2f\left(-3\right)=42$
    $\to f\left(-3\right)=-\dfrac{28}5$

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