3f(x)+2f(x分之一)=2x则f(x)=
问题描述:
3f(x)+2f(x分之一)=2x则f(x)=
答
3f(x) + 2f(1/x) = 2x...(1)
令y = 1/x
则有:3f(1/y) + 2f(y) = 2/y,即3f(1/x) + 2f(x) = 2/x...(2)
由(1)和(2)解得f(x) = 6x/5 - 4/(5x)