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

1 Answer
Jun 11, 2018

Answer:

#(-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)#