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 15d
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 guidance1
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).
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)).
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.
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)).
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.
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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. 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.
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Evaluate Composite Functions - Special Cases
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.
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4:26Evaluating Composed Functions
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.
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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
views
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 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))
3
views
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>
a. (ƒ o g ) (2)