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The question asks to find \( (f \circ g)(4) \), where:

- \( f(x) = -3x - 4 \)
- \( g(x) = 2x^2 - 2x + 7 \)

We are asked to first calculate \( g(4) \) and then plug the result into \( f(x) \).

### Step 1: Calculate \( g(4) \)
Using the function \( g(x) = 2x^2 - 2x + 7 \):

\[
g(4) = 2(4)^2 - 2(4) + 7
\]
\[
g(4) = 2(16) - 8 + 7 = 32 - 8 + 7 = 31
\]

### Step 2: Calculate \( f(g(4)) = f(31) \)
Now, using \( f(x) = -3x - 4 \), we plug in \( g(4) = 31 \):

\[
f(31) = -3(31) - 4
\]
\[
f(31) = -93 - 4 = -97
\]

Thus, \( (f \circ g)(4) = -97 \).

The correct answer is **D. -97**.

Would you like more details on any part of this solution?

### Related Questions:
1. What is the domain of \( f \circ g(x) \)?
2. Can you find \( (g \circ f)(4) \) using the same functions?
3. How do the graphs of \( f(x) \) and \( g(x) \) differ?
4. What is the range of \( f(x) \) given the domain \( x \geq 0 \)?
5. How would the composition \( (f \circ g)(x) \) change if \( g(x) \) was a linear function?

### Tip:
When solving function compositions, always start by evaluating the innermost function first before substituting its result into the outer function.

Find (f o g)(4) when f(x) = -3x - 4 and g(x) = 2x^2 - 2x + 7.

Solve the function composition problem (f o g)(4) with f(x) = -3x - 4 and g(x) = 2x^2 - 2x + 7. This step-by-step solution explores quadratic and linear functions, ideal for high school students in Grades 9-12.

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