Alright, lets get started.
The given function is :
[tex] f(x) = x + 4x^{2} - 36 [/tex]
When we find the domain of any function, we consider the domian is set of input values for which function should remain real and defined.
In this given function , we have not given any points where function seems going undefined.
Hence the domain is : (-∞, +∞) : Answer
Hope it will help :)