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.

Explore how to find the expression for (f+g)(x) using functions f(x) = x + 5 and g(x) = 3x^2. Step-by-step solution includes adding functions, simplifying terms, and understanding the result (f+g)(x) = 3x^2 + x + 5. Suitable for Grades 7-9.

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