(1)若f(x)满足2f(x)+f(1/x)=3x,求f(x).

(1)若f(x)满足2f(x)+f(1/x)=3x,求f(x).
(1)若f(x)满足2f(x)+f(1/x)=3x,求f(x).

(1)若f(x)满足2f(x)+f(1/x)=3x,求f(x).
2f(x)+f(1/x)=3x (1)
令x=1/x
则2f(1/x)+f(x)=3/x (2)
(1)*2-(2)
3f(x)=6x-3/x=(6x²-3)/x
所以f(x)=(2x²-1)/x