# functions and domains

• Sep 1st 2008, 06:30 AM
sjenkins
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.
• Sep 1st 2008, 06:41 AM
Moo
Quote:

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 ? (Wondering)

fog=f(g(x))

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

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

Then simplify.
It will be exactly the same reasoning for gof and fof
• Sep 1st 2008, 06:45 AM
sjenkins
Moo, you're always here helping me out. Thanks so much!(Rofl)

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.
• Sep 1st 2008, 07:04 AM
skeeter
try this ...

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

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