To solve $(g \circ h)(-3)$, we need to understand that this notation represents the composition of functions, specifically $g(h(-3))$.

Given:

• $g(x) = 2x + 1$
• $h(x) = 4x - 4$

Step 1: Find $h(-3)$

Substitute $-3$ into $h(x)$: $h(-3) = 4(-3) - 4 = -12 - 4 = -16$

Step 2: Substitute $h(-3)$ into $g(x)$

Now, we take the result from $h(-3)$ and substitute it into $g(x)$: $g(-16) = 2(-16) + 1 = -32 + 1 = -31$

Final Answer:

$(g \circ h)(-3) = -31$

So, the correct answer is: C) -31

Would you like further details or have any questions?

Here are some related questions that expand on this concept:

1. How do we determine the composition of two functions in general?
2. What are some real-life applications of function composition?
3. How would the solution change if the functions $g(x)$ and $h(x)$ were different?
4. How can we graphically interpret the composition of functions?
5. What are common errors when performing function composition?

Tip: When dealing with function compositions, always start with the innermost function first, and work outwards.