Question

设f(x)=x/(x-1) (x≠0,1),求f(1/f(x))

Answer 1

1/f(x)=(x-1)/x；现在就是把这个去替换自变量x；

即是

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

所以f(1/f(x))=1-x