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

Answer 1

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

The values that you can enter for x to get a finite answer are the domain of a function.

The numerator (2x+1) has no infinities or anything of the sort, so we can consider the denominator and numerator separately. We can plug in any number here and it will work!

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)#.

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Answer 2

Nathan Axel

The domain of (f(x) = \frac{2x + 1}{x - 3}) is all real numbers except (x = 3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.