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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![**Problem Statement:**
Find the domain of the function.
\[ f(x) = \sqrt{-7x + 14} \]
Write your answer using interval notation.
**Explanation:**
To determine the domain of the function \( f(x) = \sqrt{-7x + 14} \), we need to find the values of \( x \) that make the expression under the square root non-negative, as the square root of a negative number is not defined in the set of real numbers.
1. Set the expression inside the square root greater than or equal to zero:
\[
-7x + 14 \geq 0
\]
2. Solve for \( x \):
\[
-7x \geq -14
\]
Divide both sides by -7 (remember to reverse the inequality sign when dividing by a negative number):
\[
x \leq 2
\]
3. The domain in interval notation is:
\[
(-\infty, 2]
\]
**Graphical Explanation:**
- The provided interface includes options for interval notation symbols such as different types of brackets and the infinity symbol.
- There is no graph or diagram provided, only an equation and input box for solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffed13db8-c4fc-4284-8919-d62233846506%2F61cd1c04-6b43-45b6-845d-26dd97bb6824%2Fa3395fn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the domain of the function.
\[ f(x) = \sqrt{-7x + 14} \]
Write your answer using interval notation.
**Explanation:**
To determine the domain of the function \( f(x) = \sqrt{-7x + 14} \), we need to find the values of \( x \) that make the expression under the square root non-negative, as the square root of a negative number is not defined in the set of real numbers.
1. Set the expression inside the square root greater than or equal to zero:
\[
-7x + 14 \geq 0
\]
2. Solve for \( x \):
\[
-7x \geq -14
\]
Divide both sides by -7 (remember to reverse the inequality sign when dividing by a negative number):
\[
x \leq 2
\]
3. The domain in interval notation is:
\[
(-\infty, 2]
\]
**Graphical Explanation:**
- The provided interface includes options for interval notation symbols such as different types of brackets and the infinity symbol.
- There is no graph or diagram provided, only an equation and input box for solutions.
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