设函数Z=f(x,y)=xy/x2+y2,则下列个结论中不正确的是（）Af(1,y/x)=xy/x2+y2Bf(1,x/y)=xy/x2+y2Cf(1/x,1/y)=xy/x2+y2Df(x+y,x-y)=xy/x2+y2为什么选D,求详解

Question

设函数Z=f(x,y)=xy/x2+y2,则下列个结论中不正确的是（）
A f(1,y/x)=xy/x2+y2 B f(1,x/y)=xy/x2+y2 C f(1/x,1/y)=xy/x2+y2 D f(x+y,x-y)=xy/x2+y2为什么选D,求详解

Answer 1

A,把1,y/x代入,
得f(1,y/x) = (y/x) / (1 + y^2/x^2) = xy / (x^2 + y^2)
B.和A一样的方式,只是以x/y代y/x
C.把1/x,1/y代入,
f(1/x,1/y) = (1/xy) / ( 1/x^2 + 1/y^2) = xy / (x^2 + y^2)
所以A,B,C都成立.
D.
f(x+y,x-y)
= (x+y)*(x-y) / [(x+y)^2 + (x-y)^2]
= (x^2 - y^2) / (2x^2 + 2y^2)
所以D代入之后的结果不对.