# domain problem

• Sep 30th 2009, 07:23 PM
oblixps
domain problem
if the domain of f(x) is (-1,1) then what is the domain of f((x+1)/(x-1))?

i don't even know how to start this problem. all i know is that x cannot be equal to 1.
• Sep 30th 2009, 09:01 PM
mr fantastic
Quote:

Originally Posted by oblixps
if the domain of f(x) is (-1,1) then what is the domain of f((x+1)/(x-1))?

i don't even know how to start this problem. all i know is that x cannot be equal to 1.

The required domain will be the range of the function $\displaystyle y = \frac{x + 1}{x - 1}$ over the interval $\displaystyle -1 < x < 1$. The best way of finding a range is to draw a graph.
• Sep 30th 2009, 10:37 PM
A Beautiful Mind
What is this? A rational function?

'Cause the way I find is that you take the bottom part and whatever turns out to be zero is what makes the domain...

Did you need to rewrite it in a different notation?

$\displaystyle (-\infty, 1) \cup (1, \infty)$
• Sep 30th 2009, 10:38 PM
mr fantastic
Quote:

Originally Posted by A Beautiful Mind
What is this? A rational function?

'Cause the way I find is that you take the bottom part and whatever turns out to be zero is what makes the domain...

Did you need to rewrite it in a different notation?

$\displaystyle (-\infty, 1) \cup (1, \infty)$

• Oct 1st 2009, 10:16 PM
CaptainBlack
Quote:

Originally Posted by oblixps
if the domain of f(x) is (-1,1) then what is the domain of f((x+1)/(x-1))?

i don't even know how to start this problem. all i know is that x cannot be equal to 1.

The domain of:

$\displaystyle g(x)=f\left( \frac{x+1}{x-1} \right)$

will be the set of all real numbers $\displaystyle x$ such that:

$\displaystyle y=\frac{x+1}{x-1} \in (-1,1)$

CB