Question

Find the domain of the rational function.f(x)=(x−7)/(x+8)

Answer 1

`(-\infty,-8)\cup(-8,\infty)`

Explanation:

Given the rational function:

`f(x)=(x-7)/(x+8)`

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.

`\begin{gathered} x+8=0 \\ \implies x=-8 \end{gathered}`

-8 is the excluded value of the domain.

Therefore, the domain of f(x) is:

`(-\infty,-8)\cup(-8,\infty)`