https://file.aiquickdraw.com/mathbot/file/1726665428714rxqntiwb.jpg

Let's solve the puzzle step by step, evaluating each function as required.

1. **Evaluate \( f(-2) \):**
   The function is given as \( f(x) = x^3 - 2x \).

   \[
   f(-2) = (-2)^3 - 2(-2) = -8 + 4 = -4
   \]

2. **Evaluate \( g(-10) \):**
   The function is given as \( g(x) = \frac{3x}{2} \).

   \[
   g(-10) = \frac{3(-10)}{2} = \frac{-30}{2} = -15
   \]

3. **Evaluate \( h(-1) \):**
   The function is given as \( h(x) = 2x^2 + x \).

   \[
   h(-1) = 2(-1)^2 + (-1) = 2(1) - 1 = 2 - 1 = 1
   \]

4. **Evaluate \( f(3) \):**
   The function is again \( f(x) = x^3 - 2x \).

   \[
   f(3) = 3^3 - 2(3) = 27 - 6 = 21
   \]

### Final values:
- \( f(-2) = -4 \)
- \( g(-10) = -15 \)
- \( h(-1) = 1 \)
- \( f(3) = 21 \)

The corresponding answers from the choices are:
- \( f(-2) = -4 \) → C
- \( g(-10) = -15 \) → H
- \( h(-1) = 1 \) → G
- \( f(3) = 21 \) → D

So, the 4-letter code is: **CHGD**.

Would you like further details or have any questions?

Here are 5 related questions to practice:
1. Evaluate \( f(0) \).
2. Evaluate \( g(5) \).
3. Find \( h(2) \).
4. What is the value of \( f(4) \)?
5. Solve for \( x \) if \( f(x) = 0 \).

**Tip:** Always check if functions can be simplified before solving for a specific value.

Evaluate f(-2), g(-10), h(-1), and f(3) for the given functions f(x) = x^3 - 2x, h(x) = 2x^2 + x, and g(x) = 3x/2.

Solve the function evaluation puzzle by evaluating f(-2), g(-10), h(-1), and f(3) for the functions f(x) = x^3 - 2x, h(x) = 2x^2 + x, and g(x) = 3x/2. This is a great practice problem for algebra students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation