To find the values that Patrick will calculate for $f(7)$ and $g(-3)$, we need to evaluate each function using the given expressions.

Evaluating $f(7)$

The function $f(x)$ is defined as:

$f(x) = -6 + 14x$

To find $f(7)$, substitute $x = 7$ into the function:

$f(7) = -6 + 14 \times 7$

Now, calculate the value:

$f(7) = -6 + 98 = 92$

So, $f(7) = 92$.

Evaluating $g(-3)$

The function $g(x)$ is defined as:

$g(x) = (2x + 9)^2$

To find $g(-3)$, substitute $x = -3$ into the function:

$g(-3) = (2(-3) + 9)^2$

First, calculate the expression inside the parentheses:

$g(-3) = ( -6 + 9 )^2 = (3)^2$

Now, square the result:

$g(-3) = 9$

So, $g(-3) = 9$.

Final Values

• $f(7) = 92$
• $g(-3) = 9$

Patrick will calculate the values 92 for $f(7)$ and 9 for $g(-3)$.

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Would you like more details or have any questions?

Here are some related questions that expand on this topic:

1. What is the general process for evaluating a function at a given point?
2. How would the value of $g(x)$ change if the function was $g(x) = (2x + 9)^3$ instead?
3. What are the steps to find the inverse of a function, if possible?
4. How do you determine if a function is linear or quadratic?
5. Can you explain the difference between evaluating a function and solving an equation?

Tip: When substituting values into a function, always perform operations in the correct order following the order of operations (PEMDAS/BODMAS).