𝑓(𝑥) = 𝑥 + 1 and 𝑔(𝑥) = 𝑥^2 + 𝑥
(𝒇 + 𝒈)(𝒙) = 𝒇(𝒙) + 𝒈(𝒙)

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 \( x \)).

𝑓(𝑥) = 𝑥 + 1 and 𝑔(𝑥) = 𝑥^2 + 𝑥. (𝒇 + 𝒈)(𝒙) = 𝒇(𝒙) + 𝒈(𝒙)

Learn how to add functions with a step-by-step solution to (f + g)(x) for f(x) = x + 1 and g(x) = x^2 + x. This problem demonstrates key algebraic techniques such as combining like terms and simplifying polynomials. Suitable for Grades 8-10.

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