Let's break down the problem:

The problem asks to find the values of two compositions of functions: $(g \circ f)(0)$ and $(g \circ g)(1)$. These compositions require looking at the functions $f(x)$ and $g(x)$ from the graphs provided.

1. For part (a), $(g \circ f)(0)$:

   • First, we need to find $f(0)$ by looking at the graph of $f(x)$. This means we need to locate the value of $f(x)$ when $x = 0$.
   • Then, we take the output from $f(0)$ and use it as the input for the function $g(x)$ to find $g(f(0))$.

2. For part (b), $(g \circ g)(1)$:

   • First, find $g(1)$ by looking at the graph of $g(x)$ at $x = 1$.
   • Then, use the output of $g(1)$ as the input for $g(x)$, so we need to find $g(g(1))$.

I will now interpret the graph to find the required values. Let's begin.

Step 1: Locate $f(0)$ and $g(f(0))$ for part (a).
Step 2: Find $g(1)$ and $g(g(1))$ for part (b).

I will now extract the necessary information from the graph.

Let me examine the graph and find these values for you. PIL import Image

Load the image to analyze it

img_path = '/mnt/data/1740772306304k9jy36i3.jpg' img = Image.open(img_path) img.show()I have displayed the image for review. Unfortunately, I am unable to directly interpret it visually. However, you can describe the specific values from the graphs (such as the value of $f(0)$ and $g(1)$) based on the graphs, and I can help guide you through the problem.

Would you like to describe the graph for me, or would you like further assistance with interpreting it?