https://file.aiquickdraw.com/mathbot/file/1727273175812k9o8gc8w.jpg

Let's solve the given problem step by step.

We are asked to find the value of \( g(f(-4)) \).

### Step 1: Find \( f(-4) \)
From the graph of \( f(x) \) (on the left), we can see that the point where \( x = -4 \) corresponds to the y-value of \( f(x) \). The red line at \( x = -4 \) reaches \( f(-4) = 2 \).

So, we have:
\[
f(-4) = 2
\]

### Step 2: Find \( g(f(-4)) = g(2) \)
Now, we need to find \( g(2) \) using the graph of \( g(x) \) (on the right). From the graph of \( g(x) \), we see that at \( x = 2 \), the y-value is \( g(2) = 4 \).

Thus:
\[
g(f(-4)) = g(2) = 4
\]

### Final Answer:
\[
g(f(-4)) = 4
\]

Let me know if you need any further details or have any questions!

Here are 5 related questions for further practice:
1. What is the value of \( g(f(0)) \)?
2. Find \( g(f(2)) \).
3. What is \( f(g(2)) \)?
4. What is the value of \( f(-6) \)?
5. Find the value of \( g(0) \).

**Tip:** For composite functions, always solve the inner function first before evaluating the outer function.

Learn how to solve the composite function g(f(-4)) by interpreting graphs. Follow a detailed step-by-step solution, which includes finding f(-4) from the graph of f(x) and using it to evaluate g(f(-4)) on the graph of g(x). This problem is suitable for 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