If f(x)= 1/1-x

Question

Find the composition of f(f(x)).

So I get 1/1-(1/1-x)
I'm not sure if I am putting it in my calculator correctly because I keep getting a line. Is that right? If I put it in with the parentheses differently, I get the graph of f(x)=1/x.

Does anyone know which graph is right? Thanks in advance.

Answer 1

How in the world can we know which problem is right? Frankly, if I were betting,

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

so f(x)=1/(1-1/(1-x))
= (1-x)/(1-x-1)=(1-x)/(-x)= (x-1)/x

check that, it is easy to make an error typing these.

Answer 2

It wouldn't be 1/1-(1/1-x)...it would be 1/1 * (1/1-x)