Question

найти f если f(1/x) + 2f(x) = 3/x

Answer 1

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

замена x на 1/x

$fleft(xright) + 2fleft( frac{1}{x} right) }=3x$

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

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

+_____________

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

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