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Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the gridlines.)
f(g(2))

We are tasked with evaluating \( f(g(2)) \), using the given graphs of the functions \( f(x) \) and \( g(x) \).

### Step 1: Find \( g(2) \)
From the graph of \( g(x) \) (the blue curve), we observe the value of \( g \) at \( x = 2 \).
- Locate \( x = 2 \) on the horizontal axis.
- From the graph, the value of \( g(2) \) is approximately 0.

So, \( g(2) = 0 \).

### Step 2: Find \( f(g(2)) = f(0) \)
Now, we need to find \( f(0) \) using the graph of \( f(x) \) (the red line).
- Locate \( x = 0 \) on the horizontal axis.
- From the graph, the value of \( f(0) \) is 2.

Therefore, \( f(g(2)) = f(0) = 2 \).

### Final Answer:
\( f(g(2)) = 2 \).

Would you like further explanation or details on this? Here are some related questions you might find useful:

1. How do we evaluate nested functions using graphs?
2. What are some common mistakes when interpreting graphs?
3. How can we interpret the behavior of \( f(x) \) for values near \( x = 0 \)?
4. What is the significance of function composition in calculus?
5. How do transformations affect the graph of a function?

**Tip:** When evaluating composite functions graphically, always start from the inner function and use its output as the input for the outer function.

Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the gridlines.) f(g(2))

Learn how to evaluate the composite function f(g(2)) using graphs. This problem involves interpreting graphs of functions and applying the function composition theorem. Suitable for students in Grades 9-11.

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