# How do you find the domain of f(x) = 6/( x-4)?

Apr 27, 2018

$x \in \mathbb{R} , x \ne 4$

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

$\text{solve "x-4=0rArrx=4larrcolor(red)"excluded value}$

$\Rightarrow \text{domain } x \in \mathbb{R} , x \ne 4$

$x \in \left(- \infty , 4\right) \cup \left(4 , \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$
graph{6/(x-4) [-10, 10, -5, 5]}