To find the domain of a function, we need to determine the values of x for which the function is defined.
In this case, we need to make sure that the function is defined for all real numbers, except for any values of x that would result in division by zero or taking the square root of a negative number (if applicable).
The given function, f(x) = x + 7x^2 - 144, does not involve any division or square roots. Therefore, it is defined for all real numbers.
So, the domain of the function f(x) = x + 7x^2 - 144 is (-∞, ∞).
Answer: (-∞, ∞)