Question

f（x）+2f（-x）=x²+2x求f（x）的解析式要有过程

Answer 1

解由f（x）+2f（-x）=x²+2x.................①
用-x代替x代入①
得f（-x）+2f（x）=x²-2x.................②
由②×2-①
得3f(x)=x^2-6x
解得f(x)=x^2/3-2x.

Answer 2

f(x)+2f(-x)=x^2+2x ,这个式子应该对任意实数 x 都成立,
因此把 x 换成 -x 也成立,即 f(-x)+2f(x)=(-x)^2+2(-x)=x^2-2x ,
①-②×2 得 -3f(x)= -x^2+6x ,
因此解得 f(x)= 1/3*x^2-2x

Answer 3

f（x）+2f（-x）=x²+2x…………。(1)
f（-x）+2f（x）=x²-2x.................(2)
(2)*2-(1)得
3f（x）＝x²-6x
f（x）=1/3*x²-2x

Answer 4

f（x）+2f（-x）=x²+2x ......(1)
令x=-x，得：
f(-x)+2f(x)=x²-2x ......(2)
(2)*2-(1)得：
3f(x) = 2x²-4x-x²-2x = x²-6x
f(x) = 1/3x²-2x