https://file.aiquickdraw.com/mathbot/file/1725503878184sgwfqd4p.jpg

Let's analyze the problem from the image:

The given functions are:

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

We are tasked with finding \( g(f(-3)) \).

### Step 1: Find \( f(-3) \)

To calculate \( f(-3) \), substitute \( x = -3 \) into the function \( f(x) \):

\[
f(-3) = (-3)^2 + 3(-3) - 7
\]
\[
f(-3) = 9 - 9 - 7
\]
\[
f(-3) = -7
\]

### Step 2: Find \( g(f(-3)) = g(-7) \)

Now, substitute \( -7 \) into the function \( g(x) \):

\[
g(-7) = 3(-7) - 4
\]
\[
g(-7) = -21 - 4
\]
\[
g(-7) = -25
\]

Thus, \( g(f(-3)) = -25 \).

### Final Answer: d) -25

Would you like further explanation on any step?

Here are five related questions for you to explore:
1. What happens if \( f(x) \) is a different quadratic equation, like \( f(x) = x^2 - 4x + 2 \)?
2. How would the result change if the linear function \( g(x) \) were modified to \( g(x) = 2x + 1 \)?
3. What is the general approach for solving composite functions like \( g(f(x)) \)?
4. How does the domain of \( f(x) \) affect the composite function \( g(f(x)) \)?
5. What would \( g(f(x)) \) be if \( f(x) = x \) and \( g(x) = x \)? 

### Tip: 
When solving composite functions, always ensure you evaluate the inner function first and then substitute the result into the outer function for accurate results.

If f(x) = x^2 + 3x - 7 and g(x) = 3x - 4, then g(f(-3)) = ?

Learn how to solve the composite function problem where f(x) = x^2 + 3x - 7 and g(x) = 3x - 4. This detailed step-by-step solution helps understand key concepts in algebra, including quadratic and linear functions. Suitable for students in Grades 9-11.

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