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.

Answered: . Consider the function f: N – N…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.

Expert Solution

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.