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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Question
Please explain with the examples with the problem.
![**Problem Statement:**
For the function \( f(x) = \sqrt[3]{-10x + 155} \), find \( f(3) \).
(Enter your answer as \(\emptyset\) if the function does not have a value at \( x = 3 \).)
---
**Solution Explanation:**
To find the value of \( f(3) \), substitute \( x = 3 \) into the function:
\[ f(3) = \sqrt[3]{-10(3) + 155} \]
1. Calculate inside the cube root:
\[-10(3) = -30 \]
\[-30 + 155 = 125 \]
2. Evaluate the cube root:
\[ \sqrt[3]{125} = 5 \]
Therefore, \( f(3) = 5 \).
The function has a value at \( x = 3 \), and it is 5. There is no need to enter \(\emptyset\) as the function is defined at this point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F322e30c4-04c1-4495-b21b-e5cf49b8347a%2F1b179a1c-e798-4f1b-b405-fc07a16b8278%2F9szdyfi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
For the function \( f(x) = \sqrt[3]{-10x + 155} \), find \( f(3) \).
(Enter your answer as \(\emptyset\) if the function does not have a value at \( x = 3 \).)
---
**Solution Explanation:**
To find the value of \( f(3) \), substitute \( x = 3 \) into the function:
\[ f(3) = \sqrt[3]{-10(3) + 155} \]
1. Calculate inside the cube root:
\[-10(3) = -30 \]
\[-30 + 155 = 125 \]
2. Evaluate the cube root:
\[ \sqrt[3]{125} = 5 \]
Therefore, \( f(3) = 5 \).
The function has a value at \( x = 3 \), and it is 5. There is no need to enter \(\emptyset\) as the function is defined at this point.
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