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Find the inverse of the function f(x) = x². f- (7) The domain of f- is |

Find the inverse of the function f(x) = x². f- (7) The domain of f- is |

Algebra and Trigonometry (6th Edition)
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.
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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