Answer
$(-\infty, \infty)$
Work Step by Step
The domain is the set of all possible values of x
for which the value f(x) exists (is defined).
For f(x) to be defined, the following conditions must be met:
1. The radicand $\displaystyle \frac{5}{x^{2}+36}$ must not be negative (because of the square root)
The numerator is positive.
The denominator is $ \geq $36, because $x^{2} \geq 0$,
So, it is positive.
The first condition is satisfied by all real numbers.
2. The denominator, $x^{2}+36$, must not be zero.
We already concluded that $x^{2}+36 \geq 36 > 0$, so
this condition is also satisfied by all real numbers.
Domain: $\mathbb{R}$ (all real numbers)
or
$(-\infty, \infty)$
