Answer:
(-∞, ∞)
Explanation:
As you can see for each value of x , f(x) is defined 
example , for x = -8000 , f(x) is defined to be -7999.
 for x = 0 , f(x) is defined to be 1.
 for x = 8000 , f(x) is defined to be 8001.
Also,
By its graph , Which is a straight line , So, it is defined everywhere 
Thus,
 its domain is (-∞, ∞)