Express the rule in function notation. (For example, the rule "square, then subtract 5" is expressed as the function Rx) = x - 5.) Add 8, take the square root, then divide by 2. A(x) =
Express the rule in function notation. (For example, the rule "square, then subtract 5" is expressed as the function Rx) = x - 5.) Add 8, take the square root, then divide by 2. A(x) =
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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![**Understanding Function Notation: Formulating a Mathematical Rule**
**Objective:**
To express a given mathematical rule in function notation.
**Instructions:**
The rule provided should be formulated as a function. For example, the rule "square, then subtract 5" can be written as the function \( f(x) = x^2 - 5 \).
**Given Rule:**
"Add 8, take the square root, then divide by 2."
**Solution:**
1. **Add 8:** Start with the input value \( x \) and add 8 to it.
2. **Square Root:** Take the square root of the result obtained in step 1.
3. **Divide by 2:** Finally, divide the result obtained in step 2 by 2.
To express this in function notation, we perform the following transformations step-by-step:
\( x \) + 8
\[ \sqrt{x + 8} \]
\[ \frac{\sqrt{x + 8}}{2} \]
So, the function \( f(x) \) can be written as:
\[ f(x) = \frac{\sqrt{x + 8}}{2} \]
**Conclusion:**
The function that represents the rule "Add 8, take the square root, then divide by 2" is:
\[ f(x) = \frac{\sqrt{x + 8}}{2} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26522578-6957-488e-b440-649df0842474%2F9b7d0e8a-0b5f-4c78-af9d-e1fb0dfe6a4b%2Fi3kfemt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Function Notation: Formulating a Mathematical Rule**
**Objective:**
To express a given mathematical rule in function notation.
**Instructions:**
The rule provided should be formulated as a function. For example, the rule "square, then subtract 5" can be written as the function \( f(x) = x^2 - 5 \).
**Given Rule:**
"Add 8, take the square root, then divide by 2."
**Solution:**
1. **Add 8:** Start with the input value \( x \) and add 8 to it.
2. **Square Root:** Take the square root of the result obtained in step 1.
3. **Divide by 2:** Finally, divide the result obtained in step 2 by 2.
To express this in function notation, we perform the following transformations step-by-step:
\( x \) + 8
\[ \sqrt{x + 8} \]
\[ \frac{\sqrt{x + 8}}{2} \]
So, the function \( f(x) \) can be written as:
\[ f(x) = \frac{\sqrt{x + 8}}{2} \]
**Conclusion:**
The function that represents the rule "Add 8, take the square root, then divide by 2" is:
\[ f(x) = \frac{\sqrt{x + 8}}{2} \]
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