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!