Question

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

• A. $f$ and $g$ should be injective and surjective respectively
• B. $g$ should be injective and surjective
• C. f should be injective and surjective
• D. None of them may be surjective and injective

Answer 1

Answer: (A)

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.