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

Given:
\[ f(x) = 2x - 6 \]
\[ g(x) = x^2 - 13x + 30 \]

The sum \( (f + g)(x) \) is calculated as follows:
\[ (f + g)(x) = f(x) + g(x) = (2x - 6) + (x^2 - 13x + 30) \]
\[ (f + g)(x) = x^2 - 11x + 24 \]

Therefore, the correct option is:
\[ \text{(a.) } x^2 - 11x + 24 \]

Do you have any more questions or need further details on this problem?

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Here are some related questions you might find interesting:
1. What would \( (f - g)(x) \) be?
2. How would you solve \( f(g(x)) \)?
3. Can you calculate \( (f \cdot g)(x) \)?
4. Evaluate \( (f + g)(2) \).
5. Determine \( (g \circ f)(x) \).

**Tip:** When combining functions, always carefully align terms with similar degrees (like constants with constants, linear terms with linear terms, etc.) to ensure accuracy in your result.

Given the following functions, answer the questions that follow: f(x) = 2x - 6, g(x) = x^2 - 13x + 30, h(x) = √3 - 2x, j(x) = (x-3)/2x. Solve for (f + g)(x). Options: a. x^2 - 11x + 24, b. x^2 - 15x + 36, c. -x^2 + 15x - 36, d. x^2 - 15x + 24

Explore the solution to adding two polynomial functions, f(x) = 2x - 6 and g(x) = x^2 - 13x + 30. Learn how to correctly add functions to find (f+g)(x), with detailed steps and reasoning leading to the correct option of x^2 - 11x + 24.

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