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


c. ƒ(g (4))

Verified step by step guidance

1. Step 1: Identify the value of g(4) using the graph of the function g(x). Locate x = 4 on the x-axis and find the corresponding y-value on the graph of g(x). This y-value is g(4).
2. Step 2: Once you have determined g(4), use this value as the input for the function f(x). This means you will evaluate f at the point g(4), or f(g(4)).
3. Step 3: Locate the value of g(4) on the x-axis of the graph of f(x). Find the corresponding y-value on the graph of f(x) for this x-value.
4. Step 4: The y-value you find in Step 3 is the value of f(g(4)).
5. Step 5: Summarize the process: You first found g(4) from the graph of g(x), then used this result as the input for f(x) to find f(g(4)) from the graph of f(x).

Key Concepts

Function Composition

Function composition involves combining two functions where the output of one function becomes the input of another. In this case, to find ƒ(g(4)), you first evaluate g at 4, and then use that result as the input for the function ƒ. This process is essential for understanding how functions interact and transform values.

Evaluating Functions

Evaluating a function means substituting a specific value into the function's equation to find the corresponding output. For example, if g(x) is defined, you would substitute x with 4 to find g(4). This step is crucial in function composition, as it determines the input for the next function.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of functions to extract information about their values at specific points. In this question, understanding the graphs of ƒ and g allows you to determine the values of these functions at given inputs, which is necessary for solving the composition ƒ(g(4)).