Question

se f(x)= 1/x-1 qual o valor de x de modo que f{f(x)]=1

Answer 1

f(f(x))=  1/(1/x-1)-1=( x-1)/(2-x)

f(f(x))=1         (x-1)/(2-x)=1  2x=3   x=3/2

Answer 2

Vejamos:
1=1/(1/x-1)-1
1+1=1/(1/x-1)
2=1/(1/x-1)
2(1/x-1)=1
2/x-2=1
2/x=1+2
2/x=3
2=3x>>> 3x=2>>>x=2/3
Verificando:
f(x)=1/x-1
f(2/3)=1/(2/3)-1
f(2/3)=3/2-1
f(2/3)=3/2-2/2=1/2
f(x)=1/x-1
f(1/2)=1/(1/2)-1
f(1/2)=2-1
f(1/2)=1
Abraços