The operation \((f + g)(x)\) represents the sum of the functions \(f(x)\) and \(g(x)\). Given the functions:

\[
f(x) = x^2 - x, \quad g(x) = x + \frac{3}{4}
\]

To find \((f + g)(x)\), we add the two functions together:

\[
(f + g)(x) = f(x) + g(x)
\]

Substituting the given functions:

\[
(f + g)(x) = (x^2 - x) + \left(x + \frac{3}{4}\right)
\]

Now, let's combine like terms:

\[
(f + g)(x) = x^2 - x + x + \frac{3}{4}
\]

Simplify the expression:

\[
(f + g)(x) = x^2 + \frac{3}{4}
\]

So, the resulting function \((f + g)(x)\) is:

\[
(f + g)(x) = x^2 + \frac{3}{4}
\]

Would you like more details on this problem or have any questions?

### Related Questions to Expand Understanding:

1. What is \((f - g)(x)\) for the same functions \(f(x)\) and \(g(x)\)?
2. How do you find the product of two functions, \((f \cdot g)(x)\), given \(f(x)\) and \(g(x)\)?
3. What is the domain of the function \((f + g)(x)\)?
4. How would you graph \((f + g)(x)\) and interpret its shape?
5. How can we find \((f/g)(x)\) and what restrictions are there on its domain?

**Tip:** Always combine like terms and simplify expressions when working with functions.

Learn how to find the sum of two functions, (f+g)(x), where f(x) = x² - x and g(x) = x + 3/4. This step-by-step solution simplifies the process, covering key algebraic concepts of function operations. Suitable for students in Grades 9-10.

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