已知函数fx满足2f(x)+f(-x)=x+2,则f(2)=
问题描述:
已知函数fx满足2f(x)+f(-x)=x+2,则f(2)=
答
因为2f(x) + f(-x) = x + 2,把 x = -x 代入可得:
2f(-x) + f(x) = -x + 2
则得到方程组:
2f(x) + f(-x) = x + 2
2f(-x) + f(x) = -x + 2
解得:f(x) = x + 2/3
则f(2)= 2 + 2/3 = 8/3