To find the expression for $(f + g)(x)$, we add the given functions $f(x)$ and $g(x)$.

Given: $f(x) = x + 5$ $g(x) = 3x^2$

Step 1: Write the expression for $(f + g)(x)$

$(f + g)(x) = f(x) + g(x)$ Substitute the functions: $(f + g)(x) = (x + 5) + (3x^2)$

Step 2: Simplify the expression

Combine the terms: $(f + g)(x) = 3x^2 + x + 5$

Final Answer:

The expression for $(f + g)(x)$ is $3x^2 + x + 5$.

Would you like to explore more details or have any questions?

Here are 5 related questions you might consider:

1. What is the expression for $(f \cdot g)(x)$ if $f(x) = 2x + 3$ and $g(x) = x^2 + 1$?
2. How would you solve $(f + g)(x) = 0$?
3. What is the domain of $(f + g)(x)$ when $f(x) = \frac{1}{x}$ and $g(x) = \sqrt{x}$?
4. How does the expression for $(f - g)(x)$ change if $f(x)$ is a linear function and $g(x)$ is a quadratic function?
5. How would you graph the function $(f + g)(x) = 3x^2 + x + 5$?

Tip: When adding functions, ensure that you combine like terms correctly, keeping the degree of each term in mind for accurate simplification.