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Let's start by addressing the first part of the question: finding \( (f+g)(x) \), where:

\[
f(x) = 6x + 8
\]
\[
g(x) = x + 6
\]

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

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

\[
(f+g)(x) = (6x + 8) + (x + 6)
\]

Now, simplify the expression:

\[
(f+g)(x) = 6x + x + 8 + 6
\]

\[
(f+g)(x) = 7x + 14
\]

Thus, the simplified answer is:

\[
(f+g)(x) = 7x + 14
\]

Would you like to go over the next parts of the problem (such as \( f-g \), \( fg \), and \( \frac{f}{g} \)) or focus on the domain of this function?

Here are 5 related questions you might consider:
1. How do you subtract two functions to find \( (f-g)(x) \)?
2. What happens when you multiply two functions?
3. How do you find the quotient \( \frac{f}{g}(x) \) of two functions?
4. What are the steps to determine the domain of a sum, difference, or product of functions?
5. What restrictions would you need to consider for the domain of \( \frac{f}{g} \)?

**Tip**: When determining the domain of a rational function like \( \frac{f}{g} \), always check for values of \( x \) that would make the denominator zero.

Find f + g, f − g, fg, and f/g. Determine the domain for each function. Given f(x) = 6x + 8, g(x) = x + 6.

Explore how to find the sum, difference, product, and quotient of two functions, f(x) = 6x + 8 and g(x) = x + 6. This detailed guide also covers how to determine the domain for each operation. Suitable for Grades 9-12.

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