2f(x)+x^2*f(1/x)=(3x^3-x^2+4x+3)/x+1注意有括号哦
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/26 02:38:25
2f(x)+x^2*f(1/x)=(3x^3-x^2+4x+3)/x+1注意有括号哦2f(x)+x^2*f(1/x)=(3x^3-x^2+4x+3)/x+1注意有括号哦2f(x)+x^2*f(1/x)
2f(x)+x^2*f(1/x)=(3x^3-x^2+4x+3)/x+1注意有括号哦
2f(x)+x^2*f(1/x)=(3x^3-x^2+4x+3)/x+1
注意有括号哦
2f(x)+x^2*f(1/x)=(3x^3-x^2+4x+3)/x+1注意有括号哦
2f(x)+x^2*f(1/x)=(3x^3-x^2+4x+3)/(x+1)
用1/x替换上式子中的x
2f(1/x) + f(x) /x^2 = (3/x^3 - 1/x^2 + 4/x + 3)*x/(x+1)
= (3 - x + 4x^2 + 3x^3)/[(x+1)x^2]
整理
f(x) + 2x^2 f(1/x) = (3 - x + 4x^2 + 3x^3)/(x+1)
与原方程联立,消 f(1/x)
f(x) + 2x^2 f(1/x) = (3 - x + 4x^2 + 3x^3)/(x+1)
4f(x) + 2x^2*f(1/x) = 2(3x^3-x^2+4x+3)/(x +1)
两式子相减
3f(x) = (6x^3 - 2x^2 + 8x + 6 - 3 + x - 4x^2 -3x^3)/(x+1)
= (3x^3 - 6x^2 + 9x +3)/(x+1)
所以
f(x) = (x^3 - 2x^2 + 3x +1)/(x+1)
将1/x当成x代入：
2f(1/x)+f(x)/x^2=(3/x^3-1/x^2+4/x+3)*x+1
2f(1/x)+f(x)/x^2=3/x^2-1/x+5+3x
等式两边同乘以x^2
2x^2*f(1/x)+f(x)=3-x+5x^2+3x^3
原式×2-上式：
3f(x)=(6x^2-2x+10+6/x)-(3-x+5x^2+3x^3)
f(x)=(-3x^4+x^3-x^2+7x+6)/(3x)
已知f(x)满足2f(x)+f(1/x)=3x,求f(x)
F(X)满足F(x)+2f(x分之1)=3X,求f(x)
已知f(x)满足2f(x)+f(1/x)=3x,求f(x)?
已知f(x)满足2f(x)+f(-x)=-3x+1,求f(x)
已知f(x)满足f(x)+2f(1/x)=3x,求f(x) ,
已知函数f(x)=x^3+x^2-2x-x,f(1)f(2)
f(x)满足f(-x)+2f(x)=x+3,则f(1)等于
已知f(x)+2f(1/x)=x+2/x+3,求f(x)
设f(x)={3x-1,x=0,求f(-x),f(x-2).
f(x+1)+f(x-1)=4x^3-2x求f(x)
已知f(x+1/x-1)=3f(x)-2x,求f(x)
f(1+x)+2f(1-x)=3x^2 求f(x)f(1+x)+2f(1-x)=3x^2求f(x)
f(x)+2f(1/x)=3x
f(x+2)>=f(x)+2,f(x+3)
f(x)=5x+3 f(x)=5x f(x)=x+2x+1 f(x)=5x+3 f(x)=5x f(x)=x+2x+1
f(X)=f(X+2)(x
F(x)=3x^2+2x-1 求F(x+△x)-f(x)/ △x
若f(x)满足f(x)-2f(1/x)=x,则f(x)=?