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The problem provided is as follows:

Given:
- \( f(x) = 6x + 2 \)
- \( g(x) = x - 5 \)

We are tasked with finding \( f(g(x)) \), which is the composition of the functions \( f \) and \( g \).

### Solution:

1. The composition \( f(g(x)) \) means that we substitute \( g(x) \) into \( f(x) \).

Since \( g(x) = x - 5 \), substitute this into \( f(x) \):
\[
f(g(x)) = f(x - 5)
\]

2. Now, substitute \( x - 5 \) for \( x \) in \( f(x) = 6x + 2 \):
\[
f(x - 5) = 6(x - 5) + 2
\]

3. Simplify the expression:
\[
f(x - 5) = 6x - 30 + 2
\]
\[
f(x - 5) = 6x - 28
\]

Thus, the composition \( f(g(x)) = 6x - 28 \).

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is \( g(f(x)) \) in this case?
2. If \( g(x) = 2x + 3 \), how does that change \( f(g(x)) \)?
3. How do you solve for \( f(g(x)) \) if both functions are quadratic?
4. Can you find the inverse of \( f(x) \) and \( g(x) \)?
5. How would you graph both \( f(x) \) and \( f(g(x)) \)?

**Tip**: Function composition involves plugging one function into another; simplifying carefully is key!

Given f(x) = 6x + 2 and g(x) = x - 5, find f(g(x)).

Learn how to find the composition of functions with f(x) = 6x + 2 and g(x) = x - 5. The step-by-step solution simplifies the function composition f(g(x)) with key algebraic concepts. Suitable for students in Grades 9-12.

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