Precalculus (6th Edition) Blitzer

The domain of the function $g\left( x \right)=\frac{4}{x-7}$ is $\left( -\infty,7 \right)\cup \left( 7,\infty \right)$.
Consider the given function $g\left( x \right)=\frac{4}{x-7}$. We can see that this function contains division and division by 0 is not defined, excluding those values of $x$ from the domain that cause the denominator to be zero. Thus, set the denominator equal to 0, that is, $x-7=0$. This means that $x=7$. Therefore, the domain of the given function is the set of all real numbers excluding the number 7. Thus, the domain of the function $g\left( x \right)=\frac{4}{x-7}$ is $\left( -\infty,7 \right)\cup \left( 7,\infty \right)$.