Question

af(x)+bf(1/x)=cx.(a,b,c属于R,ab不等于0,a*a不等于b*b）,求f(x).

Answer 1

af(x)+bf(1/x)=cx (1)

令m=1/x,则x=1/m

所以af(1/m)+bf(m)=c/m

所以af(1/x)+bf(x)=c/x (2)

(1)*a-(2)*b

(a²-b²)f(x)=acx-bc/x

f(x)=(acx-bc/x)/(a²-b²)