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))
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 15b
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))
Verified step by step guidance1
Identify the value of \( f(2) \) from the graph of \( f(x) \).
Substitute \( f(2) \) into the function \( g(x) \) to find \( g(f(2)) \).
Locate the value of \( g(f(2)) \) on the graph of \( g(x) \).
Verify the corresponding \( y \)-value on the graph of \( g(x) \) for the input \( f(2) \).
Conclude the process by confirming the value of \( g(f(2)) \) from the graph.
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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 combining two functions where the output of one function becomes the input of another. In this case, g(f(2)) means you first evaluate f at 2, and then take that result and use it as the input for g. Understanding how to properly execute this process is crucial for solving the problem.
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Evaluating Functions
Evaluating a function at a specific point requires substituting the input value into the function's equation or graph. For f(2), you would find the value of the function f at x = 2, which can be done by looking at the graph of f. This step is essential before proceeding to the next function in the composition.
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Graph Interpretation
Interpreting graphs is vital for understanding the behavior of functions visually. You need to analyze the graphs of f and g to find the corresponding values at specific points. This skill allows you to extract necessary information from the graphs to evaluate the functions accurately.
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06:15Graphing The Derivative
Related Practice
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Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>
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