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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![**Finding the Inverse of a Function**
For the given function \( f(x) = x^2 \), we are tasked with finding its inverse. The inverse is a function that, in this case, reverses the operation of squaring an input.
1. **Inverse Function:**
The inverse function is denoted as \( f^{-1}(x) \).
- For \( f(x) = x^2 \), the inverse function \( f^{-1}(x) \) is found to be \( -\sqrt{x} \). This suggests that the inverse operation of squaring is taking the negative square root.
2. **Domain of the Inverse Function:**
- The domain of \( f^{-1} \) needs to be determined based on the context of the inverse function. It's typically the range of the original function.
**Note:** When dealing with inverse functions of quadratics, it is important to consider the limitations due to their definitions and possible restrictions applied to ensure the inverse remains a function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48fa4630-898d-4668-bcbd-9d78703ecc6b%2F203531f2-43d7-4f6b-ad6b-4f9639281a13%2F04bygj3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Inverse of a Function**
For the given function \( f(x) = x^2 \), we are tasked with finding its inverse. The inverse is a function that, in this case, reverses the operation of squaring an input.
1. **Inverse Function:**
The inverse function is denoted as \( f^{-1}(x) \).
- For \( f(x) = x^2 \), the inverse function \( f^{-1}(x) \) is found to be \( -\sqrt{x} \). This suggests that the inverse operation of squaring is taking the negative square root.
2. **Domain of the Inverse Function:**
- The domain of \( f^{-1} \) needs to be determined based on the context of the inverse function. It's typically the range of the original function.
**Note:** When dealing with inverse functions of quadratics, it is important to consider the limitations due to their definitions and possible restrictions applied to ensure the inverse remains a function.
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