1. **State the problem:** We are given two functions $f(x) = 2x + 4$ and $g(x) = 3x^2$. We need to find the function operation $(f+g)(x)$ and then determine the domain of the resulting function. 2. **Formula and explanation:** The sum of two functions $f$ and $g$ is defined as: $$ (f+g)(x) = f(x) + g(x) $$ This means we add the outputs of $f$ and $g$ for the same input $x$. 3. **Perform the operation:** $$ (f+g)(x) = (2x + 4) + (3x^2) $$ Simplify by combining like terms: $$ (f+g)(x) = 3x^2 + 2x + 4 $$ 4. **Find the domain:** - The domain of $f(x) = 2x + 4$ is all real numbers because it is a linear function. - The domain of $g(x) = 3x^2$ is all real numbers because it is a polynomial. - The sum of two functions with domain all real numbers also has domain all real numbers. **Final answer:** $$ (f+g)(x) = 3x^2 + 2x + 4 $$ with domain $(-\infty, \infty)$ (all real numbers).