Answer:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]Explanation:
Given the rational function:
[tex]f(x)=\frac{x-7}{x+8}[/tex]The domain of f(x) is the set of the values of x for which the function is defined.
A rational function is undefined when the denominator is 0.
Set the denominator of f(x) equal to 0 in order to find the value(s) of x at which f(x) is undefined.
[tex]\begin{gathered} x+8=0 \\ \implies x=-8 \end{gathered}[/tex]-8 is the excluded value of the domain.
Therefore, the domain of f(x) is:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]
