Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Question
#### Explanation:
- \( (f \circ g)(x) \) denotes the composition of functions where \( g(x) \) is substituted into \( f(x) \).
- \( (g \circ f)(x) \) denotes the composition of functions where \( f(x) \) is substituted into \( g(x) \).
To compute these, follow these steps:
1. Substitute \( g(x) \) into the function \( f(x) \).
2. Substitute \( f(x) \) into the function \( g(x) \).
This exercise illustrates how to handle compositions of functions, a key concept in understanding how functions can interact and transform inputs through successive operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f4719ec-89c6-49f2-a8fd-c905fe776b01%2F5aa8edb4-69d8-4fd1-bfa3-5f9c8f341f10%2Fvr9xvx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Function Composition
### Instructions:
Use \( f(x) = 4x - 3 \) and \( g(x) = 2 - x^2 \) to evaluate the following expressions.
#### (a) \( (f \circ g)(x) \)
<div style="border: 1px solid black; width: 150px; height: 30px;"></div>
#### (b) \( (g \circ f)(x) \)
<div style="border: 1px solid black; width: 150px; height: 30px; background-color: lightgray;"></div>
### Additional Resources:
- [Show My Work (optional)](URL)
#### Explanation:
- \( (f \circ g)(x) \) denotes the composition of functions where \( g(x) \) is substituted into \( f(x) \).
- \( (g \circ f)(x) \) denotes the composition of functions where \( f(x) \) is substituted into \( g(x) \).
To compute these, follow these steps:
1. Substitute \( g(x) \) into the function \( f(x) \).
2. Substitute \( f(x) \) into the function \( g(x) \).
This exercise illustrates how to handle compositions of functions, a key concept in understanding how functions can interact and transform inputs through successive operations.
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