# How do you find the domain of g(x) = x/((x-1)(x+3))?

May 12, 2015

The answer is : D = RR-{-3;1}.

The domain of a function is all the values that $x$ can take.

Think about it this way : In a usual function, it is all the real numbers ($\mathbb{R}$) except some numbers or ranges of numbers. Basically, it is all the $x$ you can't use because your function wouldn't give you a finite result (it would give you $\infty$ or something you can't calculate, like $\sqrt{- 3}$).

So we have : $g \left(x\right) = \frac{x}{\left(x - 1\right) \left(x + 3\right)}$

In your case, since we have a fraction, you know you can't divide by zero.

So you will avoid having $- 3$ and $1$ as values of $x$ and exclude them from the domain :

D = RR-{-3;1} or

D = ]-oo;-3[ uu ]-3;1[ uu ]1; +oo[.