If for two functions g and f,the composite fu | vedclass

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(A) Given that $g \circ f: A 	o C$ is a bijection (both injective and surjective).$1$. For $g \circ f$ to be injective,$f$ must be injective. If $f(x

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$f$ must be injective and $g$ must be surjective.

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(A) Given that $g \circ f: A 	o C$ is a bijection (both injective and surjective).$1$. For $g \circ f$ to be injective,$f$ must be injective. If $f(x_1) = f(x_2)$,then $g(f(x_1)) = g(f(x_2))$,which implies $x_1 = x_2$ since $g \circ f$ is injective.$2$. For $g \circ f$ to be surjective,$g$ must be surjective. For every $z \in C$,there exists $x \in A$ such that $g(f(x)) = z$. This implies that for every $z \in C$,there exists $y = f(x) \in B$ such that $g(y) = z$,which is the definition of $g$ being surjective.Therefore,$f$ must be injective and $g$ must be surjective.

If for two functions $g$ and $f$,the composite function $g \circ f$ is both injective and surjective,then which of the following is true?

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