To solve for $(f + g)(x)$, we add the two given functions $f(x)$ and $g(x)$:

Given:

• $f(x) = x^2 + 7x + 10$
• $g(x) = x + 5$

Step 1: Add the functions

$(f + g)(x) = f(x) + g(x)$ Substitute the values of $f(x)$ and $g(x)$: $(f + g)(x) = (x^2 + 7x + 10) + (x + 5)$

Step 2: Combine like terms

• Combine $x^2$ terms: $x^2$
• Combine $x$ terms: $7x + x = 8x$
• Combine constant terms: $10 + 5 = 15$

Thus: $(f + g)(x) = x^2 + 8x + 15$

Final Answer:

$(f + g)(x) = x^2 + 8x + 15$

Let me know if you'd like further explanation or steps! Here are related questions to explore:

1. How do you subtract two functions, such as $(f - g)(x)$?
2. What is the general form of a quadratic equation?
3. How do you factorize $x^2 + 8x + 15$?
4. What is the vertex of the function $x^2 + 8x + 15$?
5. How do you determine the roots of a quadratic function?

Tip: When combining functions, always group similar terms (like $x$-terms, constants, etc.) for clarity!