Question

f(x)+2f(1/x)=3x,求f(x)

Answer 1

当 x = y 时:

f(y) + 2f(1/y) = 3y *

当 x = 1/y 时:

f(1/y) + 2f(y) = 3/y 2f(1/y) + 4f(y) = 6/y **

两式相减得:

-3f(y) = 3y - 6/y

f(y) = 2/y -y

即:

f(x) = 2/x - x

PS:关于补充,可以这样理解.

x = 1/y 代入表达式.

老师做这题时说f(1/y)+2f(y)=3乘1/y