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

1 Answer
Mar 13, 2018

#(-infty, 3) cup (3, infty)#


The domain of a function is the values you can plug in for x and get a finite answer.

We see can think about the denominator and numerator separately. The numerator (2x+1) doesn't have any infinities or anything. No matter what we plug in here, there is no problem!

The denominator (x-3) has a small problem at x=3: it hits zero! Dividing by zero is obviously a problem, since then the function goes to positive or negative infinity. Therefore, we know that we can plug in any number except x=3, so the domain is
#(-infty, 3) cup (3, infty)#.