The problem in the image asks to determine the composite function $f \circ g(x)$ (fog $x$) where:

• $f(x) = 3x + 1$
• $g(x) = 9x - 2$

To find $f(g(x))$, we need to substitute $g(x)$ into $f(x)$. This means wherever there is an $x$ in $f(x)$, we will replace it with $g(x)$.

Here are the steps:

1. Start with the function $f(x) = 3x + 1$.
2. Replace $x$ with $g(x)$ which is $9x - 2$.

This gives us: $f(g(x)) = 3(9x - 2) + 1$ Now, simplify the expression: $f(g(x)) = 3 \cdot 9x - 3 \cdot 2 + 1 = 27x - 6 + 1 = 27x - 5$

Thus, the composite function $f \circ g(x)$ is: $f(g(x)) = 27x - 5$

Let me know if you need any more details or have questions!

Here are some related questions:

1. How do you find the composite function of $g \circ f(x)$?
2. What are the conditions for two functions to be invertible?
3. How does the order of composition affect the result of composite functions?
4. What happens when you compose a function with its inverse?
5. Can you have multiple solutions for a composite function?

Tip: When working with composite functions, always ensure you substitute carefully and simplify step by step to avoid errors.