Given the functions $f(x) = x + 1$ and $g(x) = x^2 + x$, we need to find $(f + g)(x)$, which is the sum of $f(x)$ and $g(x)$.

Step-by-Step Solution:

$(f + g)(x) = f(x) + g(x)$ Substitute $f(x) = x + 1$ and $g(x) = x^2 + x$: $(f + g)(x) = (x + 1) + (x^2 + x)$

Now, combine like terms: $(f + g)(x) = x^2 + x + x + 1 = x^2 + 2x + 1$

Thus, the result is: $(f + g)(x) = x^2 + 2x + 1$

Would you like further details or explanations?

Here are 5 related questions:

1. What is the derivative of $(f + g)(x)$?
2. What is $(f \cdot g)(x)$?
3. How would you solve $(f + g)(x) = 0$?
4. What happens if you evaluate $(f + g)(x)$ at a specific value of $x$, like $x = 2$?
5. How would you find $(f - g)(x)$?

Tip: When adding or subtracting functions, always combine like terms (same powers of $x$).