We are asked to find $(f \circ g)(-6)$, which is the composition of the functions $f(x)$ and $g(x)$.

Given:

• $f(x) = 2x + 1$
• $g(x) = 3x - 5$

The composition $(f \circ g)(x)$ means applying $g(x)$ first, then applying $f$ to the result of $g(x)$. So we need to compute $f(g(-6))$.

Step-by-step solution:

1. First, calculate $g(-6)$: $g(-6) = 3(-6) - 5 = -18 - 5 = -23$

2. Now, compute $f(g(-6)) = f(-23)$: $f(-23) = 2(-23) + 1 = -46 + 1 = -45$

Thus, $(f \circ g)(-6) = -45$.

Do you want more details or have any questions about this?

Here are some related questions to further explore:

1. What is $(g \circ f)(x)$ and how is it different from $(f \circ g)(x)$?
2. How would you solve $(f \circ f)(x)$ with the given $f(x) = 2x + 1$?
3. Can you find the inverse of $f(x)$ or $g(x)$?
4. How does the order of composition affect the outcome when combining functions?
5. How would the result change if we evaluated $(g \circ f)(-6)$?

Tip: Always apply the inner function first when dealing with compositions of functions.