Question: Prove the following statements about the functions: (explain each step and if possible explain using coq language) The function f ( x ) = x

Prove the following statements about the functions: (explain each step and if possible explain using coq language)

The function f (x) = x2 for x N is injective, but not surjective.

The constant function f (x) = c for x N is not injective or surjective.

The inverse of a bijective function is bijective.

The composition of two bijective functions is bijective.

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