Q1.f:R--->R satisfies the condition x²f(x)+f(1-x)=2x-x⁴.find f(x) and its domain and range

Let us put x as (1-x).

thus we have the equation:

(1-x)^2 f(1-x)+f(1-(1-x))=2(1-x)-(1-x)^4

=> (1-x)^2 f(1-x)+f(x)=2(1-x)-(1-x)^4--------------------------------1)

=> x^2f(x)+f(1-x)=2x-x^4-------------------------------------2)

(the original equation)

multiply 2) by by -(1-x)^2 and solving both the eqns simultanously

we get  a very wierd expn. for f(x)

f(x)=(2(1-x)-(1-x)^4-(2x-x^4)((1-x)^2))/(1-x^2(1-x)^2)

(SORRY FOR NOT SIMPLIFYING)(sorry for usage of bad font as im restricted with not a very mathematical font )

the domain is i guess all real values except (1+ srqt(5))/2 and (1- srqt(5))/2

Please be kind enough to rate me for this as it has taken me quite a bit of patience to solve this one