Find the entire domain on which the function f is one-to-one and nor decreasing. Write the domain in interval notation. f(x) = x2 - 3 (0,00) Find the inverse of f restricted to that domain. f-1(x) = Vx + 3
Find the entire domain on which the function f is one-to-one and nor decreasing. Write the domain in interval notation. f(x) = x2 - 3 (0,00) Find the inverse of f restricted to that domain. f-1(x) = Vx + 3
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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![**Problem Statement:**
Find the entire domain on which the function \( f \) is one-to-one and non-decreasing. Write the domain in interval notation.
**Function:**
\[ f(x) = x^2 - 3 \]
**Incorrect Attempt:**
\[ (0, \infty) \; \times \]
**Next Task:**
Find the inverse of \( f \) restricted to that domain.
**Inverse Function:**
\[ f^{-1}(x) = \sqrt{x + 3} \; \checkmark \]
**Guidance:**
To help identify a domain on which the function is non-decreasing, determine an interval on the x-axis for which the function values increase as the x-values increase. Graphing the function may be useful. How does restricting the domain to this interval make the function one-to-one? How does the restricted domain determine which root, positive or negative, should be considered when finding the inverse of the quadratic function?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8880cc9-7507-4211-ae45-e658bf42d6a0%2F0befe6d0-6cab-418f-8ea7-7190d52ef417%2F47q4rt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the entire domain on which the function \( f \) is one-to-one and non-decreasing. Write the domain in interval notation.
**Function:**
\[ f(x) = x^2 - 3 \]
**Incorrect Attempt:**
\[ (0, \infty) \; \times \]
**Next Task:**
Find the inverse of \( f \) restricted to that domain.
**Inverse Function:**
\[ f^{-1}(x) = \sqrt{x + 3} \; \checkmark \]
**Guidance:**
To help identify a domain on which the function is non-decreasing, determine an interval on the x-axis for which the function values increase as the x-values increase. Graphing the function may be useful. How does restricting the domain to this interval make the function one-to-one? How does the restricted domain determine which root, positive or negative, should be considered when finding the inverse of the quadratic function?
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