https://file.aiquickdraw.com/mathbot/file/1728597036979at9du9q3.jpg

Let's go through the problem step-by-step, using the graphs of \( f(x) \) and \( g(x) \).

1. **For \( f(g(1)) \)**:
   - First, find \( g(1) \) from the graph of \( g(x) \). At \( x = 1 \), the value of \( g(1) \) is 0 (from the graph of \( g(x) \)).
   - Now, substitute \( g(1) = 0 \) into \( f(x) \), so we need to find \( f(0) \).
   - From the graph of \( f(x) \), at \( x = 0 \), \( f(0) = 3 \).

   Therefore, \( f(g(1)) = 3 \).

2. **For \( g(f(3)) \)**:
   - First, find \( f(3) \) from the graph of \( f(x) \). At \( x = 3 \), the value of \( f(3) \) is 4.
   - Now, substitute \( f(3) = 4 \) into \( g(x) \), so we need to find \( g(4) \).
   - From the graph of \( g(x) \), at \( x = 4 \), \( g(4) = 3 \

Use the graphs to evaluate f(g(1)), g(f(3)), f(f(0)), g(g(4)).

Learn how to evaluate compositions of functions using graphs. This problem walks through examples such as f(g(1)), g(f(3)), f(f(0)), and g(g(4)), with detailed steps and graph interpretation. Ideal for students in Grades 9-10.

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