Patrick is practicing evaluating functions. He is using the following functions.

*f(x)* = −6 + 14*x*
*g(x)* = (2*x* + 9)2

He evaluates the functions for *f*(7) and *g*(−3). What values will he calculate?

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 \( g(-3) \).

---

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).

Learn how to evaluate functions f(x) = -6 + 14x and g(x) = (2x + 9)^2 for specific values. Understand the process and calculations for f(7) = 92 and g(-3) = 9 with detailed step-by-step solutions. Suitable for students in Grades 9-12.

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