Question

已知函数f(x)满足f(x)=2f(1/x)+x,求f(x)的解析式

Answer 1

let y=1/x

f(x) =2f(1/x)+x (1)

f(1/y) = 2f(y) + 1/y

f(1/x) = 2f(x) + 1/x (2)

sub (2) into (1)

f(x) = 2[2f(x) +1/x] +x

-3f(x)= 2/x +x

f(x) = (-1/3)(2/x+x)