Textbook Question
Use the table to evaluate the given compositions. <IMAGE>
g(ƒ(4))
2
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Ch. 1 - Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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Table of contents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Not the one you use?Change textbook
Chapter 1, Problem 15e
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 guidance1
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).
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)).
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.
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.
Step 5: Conclude by stating the value of f(f(8)) based on the graph analysis.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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Evaluate Composite Functions - Special Cases
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.
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4:26Evaluating Composed Functions
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.
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06:15Graphing The Derivative
Related Practice
Textbook Question
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))
Textbook Question
Use the table to evaluate the given compositions. <IMAGE>
g(h(ƒ(4)))
1
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Textbook Question
Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>
b. g (ƒ (2))
Textbook Question
Use the table to evaluate the given compositions. <IMAGE>
h(h(h(0)))
Textbook Question
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))
1
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