Question

найти f если f(1/x) + 2f(x) = 3/x

Answer 1

$f\left( \frac{1}{x} \right) + 2f(x) = \frac{3}{x}$

замена x на 1/x

$f\left(x\right) + 2f\left( \frac{1}{x} \right) }=3x$

$\begin{cases}f\left( \frac{1}{x} \right) + 2f(x) = \frac{3}{x}\ /\cdot(-2)\\ f\left(x\right) + 2f \left(\frac{1}{x} \right) =3x\end{cases}$

$\begin{cases}-2f\left( \frac{1}{x} \right)-4f(x) =- \frac{6}{x}\\ f\left(x\right) + 2f \left(\frac{1}{x} \right) =3x\end{cases}$

+_____________

$-3f(x)=- \frac{6}{x}+3x\ /:(-3)$

$f(x)=\frac{2}{x}-x$