For the function f(x) = -10x + 155, find f(3). (Enter your answer as if the function does not have a value at x = 3.)

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**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.
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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