how do you find the domain of the function::

Question

14/(x^2 - 361) <-- this is all under a square root..

i have attempted this so many times and have not found the correct answer yet. how do i solve the domain when it is a square root function with a denominator???? please help!

thanks

Answer 1

Two conditions are the problem here:
1. We cannot divide by zero
2. We cannot take the square root of a negative.

so 14/√(x^2 - 361)
= 14/√[(x+19)(x-19)]
so clearly x cannot be ± 19

secondly, wouldn't the number under the root sign be negative for all values between 1- and +19

so the domain is
x > 19 OR x < -19 , x is a real number.