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If F : A → A, G : A → A Are Two Bijections, Then Prove That Fog Is a Surjection ? - Mathematics

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Question

If f : A → Ag : A → A are two bijections, then prove that fog is a surjection ?

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Solution

Given: A → Ag : A → A are two bijections.
Then,  fog : A → A

Surjectivity of fog:
Let z be an element in the co-domain of fog (A).

Now, ∈ (co-domain of f) and f is a surjection.

So, f(y), where y ∈ (domain of f) ...(1)

Now, y(co-domain of g) and g is a surjection.So, y=g(x), where x(domain of g)         ...(2)

From (1) and (2),

(y((x)(fog(x), where ∈ A   (domain of fog)

So,  fog is a surjection.

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Chapter 2: Functions - Exercise 2.4 [Page 69]

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RD Sharma Mathematics [English] Class 12
Chapter 2 Functions
Exercise 2.4 | Q 24.2 | Page 69

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