proof question please see the picture , thanks.Let f : A ! B be a function and let S be a subset of A.(i) Show that S f?1(f(S)).(ii) If f is one-to-one, show that S = f?1(f(S)). 3. Let f: A B be a function and let S be a subset of A.(i) Show that S ℃ ƒ−¹(ƒ(S)).(ii) If ƒ is one-to-one, show that S = ƒ−¹(ƒ(S)).

Given- Let f : A → B be a function and let S be a subset of A. To Show- Show that S ⊂ f-1fS. If f…

Answered: 3. Let f A → B be a function and let S…

3. Let f A → B be a function and let S be a subset of A. (i) Show that S c ƒ˜¹ (ƒ(S)). (ii) If f is one-to-one, show that S = ƒ−¹(ƒ(S)).

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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Question

proof question

please see the picture , thanks.

Let f : A ! B be a function and let S be a subset of A.

(i) Show that S f?1(f(S)).

(ii) If f is one-to-one, show that S = f?1(f(S)).

3. Let f: A B be a function and let S be a subset of A.
(i) Show that S ℃ ƒ−¹(ƒ(S)).
(ii) If ƒ is one-to-one, show that S = ƒ−¹(ƒ(S)).

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