3. Let f: A –→ B be an invertible function. Prove that f is surjective. 4. Show that both equations in the definition of invertibility are necessary. In other words, find a noninvertible function f1: A → B for which there is a function gi: B → A satisfying g1 o fi = idA, and a different noninvertible function f2: A → B for which there is a function g2: B→ A satisfying f2 o g2 = idB. To argue that your functions fi and f2 are not invertible, you may want to use the result of the previous problem and the related result about injectivity from class.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please write up proofs for the following problems. I need to answer them very clearly with step by step explant please ...Needed clear proof...Will be highly appreciated..Thank You I have attached 3 and 4 simultaneously because both are related to each other, please solve 3 and then use that for 4 and solve both ... Please needed both ...
3. Let f: A –→ B be an invertible function. Prove that f is surjective.
4. Show that both equations in the definition of invertibility are necessary. In other words, find a
noninvertible function f1: A → B for which there is a function gi: B → A satisfying g1 º fi = ida,
and a different noninvertible function f2: A → B for which there is a function g2: B → A satisfying
f2 o g2 = idB. To argue that your functions fi and f2 are not invertible, you may want to use the
result of the previous problem and the related result about injectivity from class.
Transcribed Image Text:3. Let f: A –→ B be an invertible function. Prove that f is surjective. 4. Show that both equations in the definition of invertibility are necessary. In other words, find a noninvertible function f1: A → B for which there is a function gi: B → A satisfying g1 º fi = ida, and a different noninvertible function f2: A → B for which there is a function g2: B → A satisfying f2 o g2 = idB. To argue that your functions fi and f2 are not invertible, you may want to use the result of the previous problem and the related result about injectivity from class.
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