SOLUTION: Why is the domain of ln(14+x^2) ...(-inf,+inf)? I thought with domain of ln we take what is inside and set that to zero, like so. 14+x^2 = 0 x^2 = -14 x = sqrt(-14) x = DNE

Click here to see ALL problems on Functions

Question 1005778: Why is the domain of ln(14+x^2) ...(-inf,+inf)?
I thought with domain of ln we take what is inside and set that to zero, like so.
14+x^2 = 0
x^2 = -14
x = sqrt(-14)
x = DNE
so the domain doesn't exist.
Something I really dont get here
Please help
Thank you
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
I think I see the problem here
You can make as large a positive number
as you want, and you will still get a valid result
for
------------------
Also, you can make as large a negative
number ( more negative ) as you want, and you
will still get a valid result for
------------------
You will never get to be
less than , but now I'm talking
about range and not domain
-----------------------
Make sense?

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
When you solved 14+x^2 = 0 for x, you found that there were no real number solutions. There are no real numbers that make 14+x^2 = 0 true.

It turns out that x^2+14 is ALWAYS positive. Regardless of whatever real number you pick for x. So x^2+14 is never negative.

So it is impossible for ln(14+x^2) to be undefined.

That is why the domain is the set of all real numbers, which in interval notation is (-inf,+inf)