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

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