https://file.aiquickdraw.com/mathbot/file/1726683371242ub9k8sr6.jpg

Let's analyze the graphs and solve each composition of functions one by one.

### 1. \( f(g(-1)) \)

- First, we need to find \( g(-1) \) from the graph of \( g(x) \) (on the right). From the graph, when \( x = -1 \), \( g(-1) = 3 \).
- Now, use this value in \( f(x) \). We need to find \( f(3) \) from the graph of \( f(x) \) (on the left). From the graph, when \( x = 3 \), \( f(3) = 2 \).
- Therefore, \( f(g(-1)) = f(3) = 2 \).

### 2. \( g(f(-4)) \)

- First, find \( f(-4) \) from the graph of \( f(x) \) (on the left). From the graph, when \( x = -4 \), \( f(-4) = -5 \).
- Now, use this value in \( g(x) \). We need to find \( g(-5) \) from the graph of \( g(x) \) (on the right). From the graph, when \( x = -5 \), \( g(-5) = 5 \).
- Therefore, \( g(f(-4)) = g(-5) = 5 \).

### 3. \( f(f(0)) \)

- First, find \( f(0) \) from the graph of \( f(x) \) (on the left). From the graph, when \( x = 0 \), \( f(0) = -3 \).
- Now, use this value in \( f(x) \) again. We need to find \( f(-3) \). From the graph, when \( x = -3 \), \( f(-3) = 1 \).
- Therefore, \( f(f(0)) = f(-3) = 1 \).

### 4. \( g(g(-3)) \)

- First, find \( g(-3) \) from the graph of \( g(x) \) (on the right). From the graph, when \( x = -3 \), \( g(-3) = 3 \).
- Now, use this value in \( g(x) \) again. We need to find \( g(3) \). From the graph, when \( x = 3 \), \( g(3) = -3 \).
- Therefore, \( g(g(-3)) = g(3) = -3 \).

### Final Answers:
1. \( f(g(-1)) = 2 \)
2. \( g(f(-4)) = 5 \)
3. \( f(f(0)) = 1 \)
4. \( g(g(-3)) = -3 \)

Do you want any detailed explanations for these steps? 

Here are 5 related questions for further exploration:
1. What is \( f(g(2)) \)?
2. What is \( g(f(-2)) \)?
3. Find \( f(g(0)) \).
4. Calculate \( f(f(4)) \).
5. Determine \( g(f(2)) \).

**Tip**: When working with compositions of functions, always evaluate the inner function first before moving to the outer one!

Use the graphs of f(x) and g(x) to evaluate the following function compositions: f(g(-1)), g(f(-4)), f(f(0)), and g(g(-3)).

Learn how to solve function compositions using graphs of f(x) and g(x). This problem covers key concepts such as function composition and graph interpretation, and provides step-by-step solutions to f(g(-1)), g(f(-4)), f(f(0)), and g(g(-3)). Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation