f(x,y)=x+2y,求f(xy,f(x,y))

题目

f(x,y)=x+2y,求f(xy,f(x,y))
f(x+y,y/x)=x^2-y^2,求f(x,y)

答案

xy+2(x+2y)
=xy+2x+4y
令x+y=m y/x=n
联立解得
x=m/(n+1) y=mn/(n+1)
所以f(m,n)=x^2-y^2
=m^2(1-n^2)/(n+1)^2=m^2(1-n)/(1+n)
即f（x,y)=x^2(1-y)/(1+y)