Question
If $g \circ f$ is bijective, then $f$ is injective and $g$ is surjective.
Step 1
This means that for any $x_1, x_2$ in the domain of $f$, if $f(x_1) = f(x_2)$, then $g(f(x_1)) = g(f(x_2))$. Since $g \circ f$ is bijective, this implies that $x_1 = x_2$. Therefore, $f$ is injective. Show more…
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