1. ## functions and domains

I think I must have missed something along the way. Can someone please explain to me step by step how to solve this?

f(x)=1/(x-1), g(x)=(x-1)/(x+1). Find fog gof, fof, gog and their domains.

First of all, I don't think I even grasp the concept of multiplying with x? I'm very confused and need some serious help. I cannot do functions.

2. Originally Posted by sjenkins
I think I must have missed something along the way. Can someone please explain to me step by step how to solve this?

f(x)=1/(x-1), g(x)=(x-1)/(x+1). Find fog gof, fof, gog and their domains.

First of all, I don't think I even grasp the concept of multiplying with x? I'm very confused and need some serious help. I cannot do functions.
Multiplying with x ?

fog=f(g(x))

So consider $f(t)=\frac{1}{{\color{red}t}-1}$ and let $t={\color{red}g(x)}$

so it'll be $\frac{1}{{\color{red}\tfrac{x-1}{x+1}}-1}$

Then simplify.
It will be exactly the same reasoning for gof and fof

3. Moo, you're always here helping me out. Thanks so much!

Can you tell me how to simplify, that is the step that I think I must have missed years ago. I am just not understanding it.

4. try this ...

clear the fraction in the denominator by multiplying numerator and denominator of $\frac{1}{\frac{x-1}{x+1}-1}$ by $(x+1)$, then simplify.

you should end up with the more simple fraction
$-\frac{x+1}{2}$