How do you find the domain of f(x) = (x-4)/(x+3)?

1 Answer
Jun 11, 2018

(-oo, -3) U (-3, oo)

Explanation:

When dealing with rational functions f(x)=(p(x))/(q(x)) , our domain, that is, values of x for which f(x) exists, excludes any values that cause q(x)=0.

This is because division by 0 isn't possible, so the function won't have any real value at these values of x.

For f(x)=(x-4)/(x+3), we have the form (p(x))/(q(x)), where p(x)=x-4, q(x)=x+3

Set q(x)=0 and solve for x:

x+3=0
x=-3

So, our domain excludes x=-3.

In interval form, the domain is

(-oo, -3) U (-3, oo)