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  4. If for two functions g and f, g o f is both injective and surjective, then which of the following is true?

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Q. If for two functions $g$ and $f, g o f$ is both injective and surjective, then which of the following is true?

Relations and Functions - Part 2

Solution:

Given that, gof is both injective and surjective.
Now, gof is injective $\Rightarrow f$ is injective and gof is surjective $\Rightarrow g$ is surjective.
Hence, $f$ and $g$ should be injective and surjective, respectively.