Let f left parenthesis x right parenthesis equals 3 x squared plus 17 x plus 20 and g left parenthesis x right parenthesis equals x plus 4. Perform the function operation and then find the domain of the result.
left parenthesis f times g right parenthesis left parenthesis x right parenthesis
To find the result of the function operation (f * g)(x), we need to multiply f(x) and g(x):
f(x) = 3x^2 + 17x + 20
g(x) = x + 4
(f * g)(x) = (3x^2 + 17x + 20)(x + 4)
(f * g)(x) = 3x^3 + 12x^2 + 17x^2 + 68x + 20x + 80
(f * g)(x) = 3x^3 + 29x^2 + 88x + 80
So, the result of the function operation is (f * g)(x) = 3x^3 + 29x^2 + 88x + 80.
To find the domain of the result, we need to consider the individual domains of f(x) and g(x). Both f(x) and g(x) are defined for all real numbers, so the domain of the result (f * g)(x) is also all real numbers.
Therefore, the domain of (f * g)(x) is all real numbers.