设函数f(x)=x/(1-x),求f[f(x)]和f{f[f(x)]}

Question

设函数f(x)=x/(1-x),求f[f(x)]和f{f[f(x)]}

Answer 1

f[f(x)]=[x/(1-x)]/[1-x/(1-x)]=x/1-2x
f{f[f(x)]}=f(x/1-2x)=[x/(1-2x)]/[1-x/(1-2x)]=x/1-3x
将f(x)看成自变量,从里往外求就可以了.