If `f: ArightarrowA ,g: ArightarrowA` are two bijections, then prove that `fog` is an injection (ii) `fog` is a surjection.

Explanation

Given: `A rightarrow A, g: A rightarrow A` are two bijections.


Then, `f circ g: A rightarrow A`


Surjectivity of fog:


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


Now, `z in A` (co-domain of `f` ) and `f` is a surjection.


So, `z=f(y)`, where `y in A` (domain of `f) ldots(1)`


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


From (1) and (2),


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