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?

Select **TWO** correct answers.

A.9

B.225

C.−28

D.104

E.92


To solve this problem, we'll evaluate both functions \( f(x) \) and \( g(x) \) for the given values \( f(7) \) and \( g(-3) \).

### Step-by-Step Evaluation:

1. **Evaluate \( f(x) = -6 + 14x \) for \( x = 7 \):**

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

Calculate:

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

So, \( f(7) = 92 \).

2. **Evaluate \( g(x) = (2x + 9)^2 \) for \( x = -3 \):**

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

Simplify inside the parentheses:

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

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

### Conclusion:

The correct answers are:

- **A. 9** (for \( g(-3) \))
- **E. 92** (for \( f(7) \))

Would you like more details or have any questions about this solution?

Here are some additional questions for practice:

1. What is the value of \( f(x) = 3x - 5 \) for \( x = 10 \)?
2. Evaluate \( g(x) = x^2 + 4x + 1 \) for \( x = -2 \).
3. Determine \( h(x) = \sqrt{x + 7} \) for \( x = 2 \).
4. If \( k(x) = 5x - 8 \), find \( k(0) \).
5. Solve for \( f(x) = 2x^2 + 3x - 4 \) when \( x = -1 \).

**Tip:** Substitute the given values into the functions and simplify step by step to evaluate correctly.

Practice evaluating functions f(x) = -6 + 14x and g(x) = (2x + 9)^2 with detailed step-by-step solutions. Learn how to calculate f(7) and g(-3) correctly. Suitable for high school students studying functions and quadratic equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation