How do you find the domain of #f(x)=(2x+1)/(x-3)#?

1 Answer
May 18, 2018

Answer:

#x in (-oo, 3) cup (3, +oo)#

Explanation:

The domain is the set of #x# values that are defined for the function #f(x)#.

Naturally a continuous function will have a domain #x in (-oo, +oo)#. However, some functions have discontinuities. These are values of #x# for which the function is not properly defined.

With rational functions, these invalid #x# values occur when the denominator is #0#, as division by zero is undefined.

We have #x-3 = 0-> x = 3# as a value of #x# that our function cannot take. We write this new domain as a combination of domains extending to infinity and containing all #x# values as close to #3# as possible without including #3# itself:

#x in (-oo, 3) cup (3, +oo)#