. Consider the function f: N – N defined by f(n) = n² . Prove that f has no right inverse, and demonstrate two distinct left inverses for f.
. Consider the function f: N – N defined by f(n) = n² . Prove that f has no right inverse, and demonstrate two distinct left inverses for f.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 54E
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Consider the function f: N⟶N defined by f(n) = n^2. Prove that f has no right inverse, and demonstrate two distinct left inverses for f.
![4. Consider the function f: N → N defined by f(n) = n². Prove that f has no right inverse, and demonstrate two distinct left inverses for f.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa55ee13-49da-4d4f-8566-873b8c782b56%2F5b1b4957-ed4a-4038-8e38-30c710116fdf%2Foxcb45e_processed.png&w=3840&q=75)
Transcribed Image Text:4. Consider the function f: N → N defined by f(n) = n². Prove that f has no right inverse, and demonstrate two distinct left inverses for f.
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Step 1
A function can have left inverse and right inverse. When these two inverse functions become equal, it is referred to as the inverse function. To exhibit a right inverse, it is necessary that the function must be bijective. Bijection is also the necessary and sufficient condition for the existence of the inverse function. Here, a function is given. We show that the function doesn't have the right inverse and find two left inverses of the function.
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