Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![The image contains handwritten mathematical functions and a query about composing them. The functions are defined as follows:
1. \( f(x) = \sqrt{x} \)
2. \( g(x) = 6x + 1 \)
The task is to find the composition of these two functions, denoted as \( (g \circ f)(x) \).
### Explanation:
- **\( f(x) = \sqrt{x} \)**: This function represents the square root of \( x \).
- **\( g(x) = 6x + 1 \)**: This is a linear function where \( x \) is multiplied by 6 and then 1 is added to the result.
### Composition of Functions:
- To find \( (g \circ f)(x) \), substitute \( f(x) \) into \( g(x) \):
\[
(g \circ f)(x) = g(f(x)) = g(\sqrt{x}) = 6(\sqrt{x}) + 1
\]
Thus, the composition \( (g \circ f)(x) \) simplifies to \( 6\sqrt{x} + 1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7b186df-8306-473e-b00b-3c96e89a3cbb%2Fb13476be-741d-42fe-90ab-c935c6032094%2Faks17s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains handwritten mathematical functions and a query about composing them. The functions are defined as follows:
1. \( f(x) = \sqrt{x} \)
2. \( g(x) = 6x + 1 \)
The task is to find the composition of these two functions, denoted as \( (g \circ f)(x) \).
### Explanation:
- **\( f(x) = \sqrt{x} \)**: This function represents the square root of \( x \).
- **\( g(x) = 6x + 1 \)**: This is a linear function where \( x \) is multiplied by 6 and then 1 is added to the result.
### Composition of Functions:
- To find \( (g \circ f)(x) \), substitute \( f(x) \) into \( g(x) \):
\[
(g \circ f)(x) = g(f(x)) = g(\sqrt{x}) = 6(\sqrt{x}) + 1
\]
Thus, the composition \( (g \circ f)(x) \) simplifies to \( 6\sqrt{x} + 1 \).
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