python - sympy solve function as function -

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i want solve f(x) 

(eq(2*f(x)+f(1/x),1/x))

the expected output

f(x) = (2-x^2)/(3*x)

i try

 solve((eq(2*f(x)+f(1/x),1/x)),f(x))

this answer contains f(1/x) : (-x*f(1/x) + 1)/(2*x)

how f(x) = (2-x^2)/(3*x) in sympy?

i don't think sympy solve functional equations in way want, separate particular equation two: 2y+z = 1/x , 2z+y = x y(1/x) = z(x) , let sympy solve both y , z:

in [5]: x, y, z = symbol('x'), symbol('y'), symbol('z') in [6]: solve((eq(2*y+z,1/x), eq(2*z+y,x)),y,z) out[6]: {y: (-x**2 + 2)/(3*x), z: (2*x**2 - 1)/(3*x)}

so y f(x) want here.


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