To solve for the values of $f(7)$ and $g(-3)$ using the given functions:

1. Function $f(x) = -6 + 14x$:

   • Substitute $x = 7$ into the function: $f(7) = -6 + 14(7) = -6 + 98 = 92$ So, $f(7) = 92$.

2. Function $g(x) = (2x + 9)^2$:

   • Substitute $x = -3$ into the function: $g(-3) = (2(-3) + 9)^2 = (-6 + 9)^2 = (3)^2 = 9$ So, $g(-3) = 9$.

Therefore, the correct answers are:

• Option A: 9
• Option C: 92

These are the values Patrick will calculate.

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

1. What is the result of $f(x) = -6 + 14x$ when $x = 0$?
2. How would the function $g(x)$ change if $x$ were 2 instead of -3?
3. How do the results change if the coefficient of $x$ in $f(x)$ is increased by 2?
4. What is the minimum value of $g(x) = (2x + 9)^2$?
5. How do the graphs of these functions look in comparison to each other?

Tip: Always verify your calculations by substituting back into the original function to ensure accuracy.