How do you find the domain of p(x) = (x-2)/3 - 1/(3x)?

Mar 29, 2018

$\left\{x \in \mathbb{R} | x \ne 0\right\}$

Explanation:

$p \left(x\right) = \frac{x - 2}{3} - \frac{1}{3 x}$

From the function we can see that the only value of $x$ for which the function is undefined is $x = 0$. this would give division by zero, which is undefined.

The domain is therefore all of $\mathbb{R}$ except $0$: We can express this as:

$\left\{x \in \mathbb{R} | x \ne 0\right\}$