# What is the domain of f(x) = 6/(4-x)?

Jan 24, 2017

$\mathbb{R} - \left\{4\right\}$

#### Explanation:

Here we have

$f \left(x\right) = \frac{6}{4 - x}$

Consider

$f \left(4\right) = \frac{6}{4 - 4} = \frac{6}{0}$ which is undefined because you can't divide by zero.

Because of this $x$ cannot take the value $4$. Since this function is defined for the rest of the Real numbers $\mathbb{R}$; we have that the domain of $f$ is $\mathbb{R} - \left\{4\right\}$ or the set of Real numbers not including four.