Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>


e. ƒ(ƒ(8))

Verified step by step guidance

1. Step 1: Identify the value of f(8) using the graph of the function f(x). Locate the point on the graph where x = 8 and find the corresponding y-value, which is f(8).
2. Step 2: Once you have determined f(8), use this value as the new input for the function f(x). This means you need to find f(f(8)).
3. Step 3: Locate the value of f(f(8)) on the graph. Use the y-value obtained from Step 1 as the x-coordinate on the graph of f(x) and find the corresponding y-value.
4. Step 4: Verify your steps by checking the graph to ensure that the values you have used and found are consistent with the graph's data.
5. Step 5: Conclude by stating the value of f(f(8)) based on the graph analysis.

Key Concepts

Function Composition

Function composition involves applying one function to the result of another function. In this case, ƒ(ƒ(8)) means you first find the value of ƒ at 8, and then use that result as the input for ƒ again. Understanding how to compose functions is crucial for solving problems that require multiple evaluations.

Function Evaluation

Function evaluation is the process of finding the output of a function for a given input. For example, to evaluate ƒ(8), you look at the graph of ƒ and find the corresponding y-value when x equals 8. This concept is fundamental in determining specific function values from their graphs.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of functions to extract information about their behavior and values. In this question, understanding how to read the graphs of ƒ and g is essential for accurately determining the function values needed for the composition. This skill is vital for connecting algebraic expressions with their graphical counterparts.