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 for function addition:** 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. **Apply the formula:** Substitute the given functions: $$ (f + g)(x) = (2x + 4) + (3x^2) $$ 4. **Simplify the expression:** Combine like terms: $$ (f + g)(x) = 3x^2 + 2x + 4 $$ 5. **Find the domain:** The domain of a function is the set of all real numbers $x$ for which the function is defined. - Both $f(x) = 2x + 4$ and $g(x) = 3x^2$ are polynomials. - Polynomials are defined for all real numbers. - Therefore, the domain of $(f + g)(x)$ is all real numbers. **Final answer:** $$(f + g)(x) = 3x^2 + 2x + 4$$ Domain: $(-\infty, \infty)$