To find $(f \circ g)(x)$, which represents the composition of the functions $f(x)$ and $g(x)$, we substitute $g(x)$ into $f(x)$. This means:

$(f \circ g)(x) = f(g(x))$

We know:

• $f(x) = 3x + 1$
• $g(x) = 2 - x$

Now substitute $g(x)$ into $f(x)$:

$f(g(x)) = f(2 - x) = 3(2 - x) + 1$

Simplifying:

$f(g(x)) = 3(2) - 3(x) + 1 = 6 - 3x + 1 = 7 - 3x$

So, $(f \circ g)(x) = 7 - 3x$.

Would you like further details or clarifications? Here are 5 related questions:

1. How do you compute the composition of two functions?
2. What happens if you reverse the order of the composition, finding $(g \circ f)(x)$?
3. How do you solve for the domain of a composed function?
4. Can you determine when $f(g(x)) = 0$?
5. What is the geometric interpretation of function composition?

Tip: When composing functions, always apply the inner function to the outer function carefully to avoid mistakes in substitution.