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


d. g(ƒ(5))

Verified step by step guidance

1. Step 1: Identify the value of f(5) using the graph of the function f. Locate the point on the graph where x = 5 and determine the corresponding y-value, which is f(5).
2. Step 2: Once you have found f(5), use this value as the input for the function g. This means you will now look for g(f(5)).
3. Step 3: Refer to the graph of the function g. Locate the point where x equals the value of f(5) that you found in Step 1.
4. Step 4: Determine the corresponding y-value on the graph of g for the x-value found in Step 3. This y-value is g(f(5)).
5. Step 5: Summarize the process: You first found f(5) from the graph of f, then used this result as the input for g to find g(f(5)) from the graph of g.

Key Concepts

Function Composition

Function composition involves applying one function to the result of another. In this case, g(f(5)) means first finding the value of f at x = 5, and then using that result as the input for the function g. Understanding how to evaluate functions in sequence is crucial for solving problems involving nested functions.

Evaluating Functions

Evaluating a function means substituting a specific input value into the function's formula or graph to find the corresponding output. For instance, to find f(5), you would locate x = 5 on the graph of f and determine the y-value at that point. This step is essential for obtaining the input needed for the next function in the composition.

Graph Interpretation

Interpreting graphs is the ability to read and understand the visual representation of functions. This includes identifying key points, such as intercepts and turning points, and understanding how the graph behaves over different intervals. In this question, accurately reading the graphs of f and g is necessary to find the correct values for the composition.