Answer
The domain of the function $g\left( x \right)=\frac{4}{x-7}$ is $\left( -\infty,7 \right)\cup \left( 7,\infty \right)$.
Work Step by Step
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 $\left( -\infty,7 \right)\cup \left( 7,\infty \right)$.
