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
![**Question: Finding the Inverse Function**
Given the function \( f(x) = 15 + \sqrt[3]{x} \), find its inverse \( f^{-1}(x) \).
**Solution:**
To find the inverse of the function, follow these steps:
1. Start with the equation \( y = 15 + \sqrt[3]{x} \).
2. Swap \( x \) and \( y \) to solve for \( y \):
\[
x = 15 + \sqrt[3]{y}
\]
3. Isolate the cube root term:
\[
\sqrt[3]{y} = x - 15
\]
4. Cube both sides to solve for \( y \):
\[
y = (x - 15)^3
\]
Thus, the inverse function is:
\[
f^{-1}(x) = (x - 15)^3
\]
**Instructions:**
- You can use a calculator to verify your result.
- Click "Check Answer" to submit your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffca48693-8901-4b5a-a0fa-df92d5d53a26%2F576089a7-1277-4b78-925e-96e9afb5e7d1%2Fujd00ns_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question: Finding the Inverse Function**
Given the function \( f(x) = 15 + \sqrt[3]{x} \), find its inverse \( f^{-1}(x) \).
**Solution:**
To find the inverse of the function, follow these steps:
1. Start with the equation \( y = 15 + \sqrt[3]{x} \).
2. Swap \( x \) and \( y \) to solve for \( y \):
\[
x = 15 + \sqrt[3]{y}
\]
3. Isolate the cube root term:
\[
\sqrt[3]{y} = x - 15
\]
4. Cube both sides to solve for \( y \):
\[
y = (x - 15)^3
\]
Thus, the inverse function is:
\[
f^{-1}(x) = (x - 15)^3
\]
**Instructions:**
- You can use a calculator to verify your result.
- Click "Check Answer" to submit your solution.
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