# Find the domain of the composite function fxg

• Oct 5th 2008, 11:15 AM
FinalFantasy9291
Find the domain of the composite function fxg
f(x)=3/x-1;g(x)=2/x

i don't get how this works..
• Oct 5th 2008, 11:29 AM
Shyam
Quote:

Originally Posted by FinalFantasy9291
f(x)=3/x-1;g(x)=2/x

i don't get how this works..

Is $\displaystyle f(x)= \frac{3}{x-1}$

or $\displaystyle \frac{3}{x}-1$ ???
• Oct 5th 2008, 11:32 AM
FinalFantasy9291
the first one
• Oct 7th 2008, 03:06 AM
Greengoblin
$\displaystyle f\circ g(x)= \frac{3}{\frac{2}{x}-1}=\frac{3x}{2}-3$

So it can accept any real or complex argument
• Oct 7th 2008, 03:12 AM
mr fantastic
Quote:

Originally Posted by Greengoblin
$\displaystyle f\circ g(x)= \frac{3}{\frac{2}{x}-1}=\frac{3x}{2}-3$

So it can accept any real or complex argument

Correction: $\displaystyle \frac{3}{\frac{2}{x}-1}= \frac{3x}{2 - x}$.
• Oct 7th 2008, 03:30 AM
Greengoblin
Ooops my mistake, so the domain is $\displaystyle \{x\in\mathbb{R}:x\ne 2\}$ that certainly makes more sense.(Giggle)