ANSWER
[tex]( - \infty , + \infty )[/tex]
EXPLANATION
The given function is
[tex]f(x) = 2 {x}^{4} + 4 {x}^{3} + 2{x}^{2} [/tex]
This is a polynomial function.
The domain refers to all real values for which the function is defined.
Polynomial functions are defined everywhere.
The domain is all real numbers.
Or
[tex]( - \infty , + \infty )[/tex]
