Question

已知函数f(x)=x/(1-x),则f[f(x)]等于多少，f{f[f(x)]}等于多少

Answer 1

已知函数f(x)=x/(1-x),

则f[f(x)]
=f[x/(1-x)]
=[x/(1-x)] / [1-[x/(1-x)]]
=[x/(1-x)] / [(1-2x)/(1-x)]
=x/(1-2x)

f{f[f(x)]}
=f[x/(1-2x)]
=[x/(1-2x)] / [1-[x/(1-2x)]]
=[x/(1-2x)] / [(1-3x)/(1-2x)]
=x/(1-3x)

希望采纳~~~

Answer 2

f[f(x)]
=[x/(1-x)]/[1-x/(1-x)]
上下乘1-x
=x/(1-2x)

f{f[f(x)]}
=f[x/(1-2x)]
=[x/(1-2x)]/[1-x/(1-2x)]
=x/(1-3x)

Answer 3

f[f(x)]=x/(1-2x)
f{f[f(x)]}=x/(1-3x)
这是口答的题目，要找到规律哟。。。

追问

已知函数f(x)=x/(1-x),则f[f(x)]等于多少，f{f[f(x)]}等于多少
请给出详细的过程，谢谢！！！

追答

这只是一个规律，记住就行了，以后看到这样的直接就写。