f(x+y,y/x)=x^2-y^2求f(x,y)
来源：学生作业帮助网 编辑：六六作业网 时间：2024/05/10 20:55:22
f(x+y,y/x)=x^2-y^2求f(x,y)f(x+y,y/x)=x^2-y^2求f(x,y)f(x+y,y/x)=x^2-y^2求f(x,y)令x+y=t,y/x=u则y=xu代入x+y=t,
f(x+y,y/x)=x^2-y^2求f(x,y)
f(x+y,y/x)=x^2-y^2
求f(x,y)
f(x+y,y/x)=x^2-y^2求f(x,y)
令x+y=t,y/x=u
则y=xu代入x+y=t,得
x+xu=t
(1) u≠-1,即y≠-x,t≠0时,
x=t/(1+u)
y=xu=ut/(1+u)
∴f(t,u)=f(x+y,y/x)=x^2-y^2=[t/(1+u)]^2-[ut/(1+u)]^2
=t^2(1-u^2)/(1+u)^2=t^2(1-u)/(1+u) （t≠0,u≠-1）
∴f(x,y)=x^2(1-y)/(1+y) (x≠0,y≠-1)
(2) u=-1时,y=-x,t=0,则
f(0,-1)=x^2-y^2=x^2-(-x)^2=0
综上可知
f(x,y)=x^2(1-y)/(1+y) (y≠-1)
=0 (y=-1)
f(x+y,x-y)=(x^2-y^2)/2xy,求f(x,y)!
f(x+y,y/x)=x^2-y^2求f(x,y)
f(x+y,y/x)=x^2-y^2,求f(x,y),详见里面
f(x+y,x-y)=2xy(x-y),求f(x,y)
f(x^2-y^2,x-y)=x+y+x^2-xy,求f'(x,y)对y求导
设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)
设f(x+y,x-y)=x^2+xy,求f(x,y)
f(x+y)=f(x)+f(y)+2xy
已知f(0)=1,f(x-y)=f(x)-y(2x-y+1),求f(x)
导数：f(x+y)=f(x)f(y),且f'(o)=1,求f'(x)f(x+y)=f(x)f(y),且f'(o)=1,求f'(x)f(x+y)=f(x)+f(y)+2xy,且f'(o)存在,求f'(x) f(1+x)=af(x),且f'(0)=b,求f'(1)
f(2x+y,2y+x)=xy,求f(x,y)
f(xy,x-y)=x^2-xy+y^2.求f(x,y)
英国数学竞赛题.f(x,x)=x,f(x,y)=f(y,x),(x+y)*f(x,y)=(2x+y)*f(x,x+y)求f(19,91)
二元函数f(x,y)=x+y/x-y,求f(y/x,x/y)
设y=f(x),f'(x)存在,求y=f(2^x)的导数
已知f(x+y)=f(x)+f(y)+2xy,求f(0)
f(x+Y)+f(x-y)=2f(x)f(Y) 求其是偶函数 急
求证f（x+y）+f(x-y)=2f(x)f(y)是周期函数