Textbook Question
Use the table to evaluate the given compositions. <IMAGE>
g(ƒ(4))
2
views
Ch. 1 - Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
Not the one you use?Change textbookSelect a different textbook
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 15c
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))
Verified step by step guidance1
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).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
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, 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.
Recommended video:
3:48
Evaluate Composite Functions - Special Cases
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.
Recommended video:
4:26Evaluating Composed Functions
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)).
Recommended video:
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>
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)
Textbook Question
Evaluate cos⁻¹(cos(5π/4)).
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>
d. g(ƒ(5))
1
views