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))

Guida verificata passo dopo passo

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).

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)).

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.

Step 4: The y-value you find in Step 3 is the value of f(g(4)).

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).

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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.

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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.

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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)).

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