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Let's solve the problem step by step.

### Given Functions:
1. \( f(x) = -6 + 14x \)
2. \( g(x) = (2x + 9)^2 \)

### Evaluate \( f(7) \):
Substitute \( x = 7 \) into the function \( f(x) \):

\[
f(7) = -6 + 14(7) = -6 + 98 = 92
\]

### Evaluate \( g(-3) \):
Substitute \( x = -3 \) into the function \( g(x) \):

\[
g(-3) = (2(-3) + 9)^2 = (-6 + 9)^2 = 3^2 = 9
\]

### Conclusion:
The values calculated are:
- \( f(7) = 92 \)
- \( g(-3) = 9 \)

So the correct answers are:
- \( 9 \) 
- \( 92 \)

These correspond to options \( A \) and \( E \).

Would you like further details or have any questions? Here are some related questions you might explore:

1. What happens to \( f(x) \) as \( x \) increases?
2. What is the effect of changing the constant in \( f(x) \) on the graph?
3. How would \( g(x) \) change if the coefficient of \( x \) were different?
4. What is the domain of the function \( g(x) \)?
5. How would you find the vertex of the quadratic function \( g(x) \)?

**Tip:** Always double-check your calculations by substituting values back into the function to ensure accuracy.

Learn how to evaluate functions f(x) = -6 + 14x and g(x) = (2x + 9)^2 with detailed step-by-step solutions. This problem covers function evaluation and quadratic equations, providing answers for f(7) = 92 and g(-3) = 9.

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