Proof: Composition of Injective Functions is Injective | Functions and Relations

Let g and f be injective (one to one) functions, where g maps A to B and f maps B to C. Then the composition fog, which maps A to C, is also injective. We'll prove this result about injective functions and their compositions in today's lesson!

The proof is very straightforward, and merely requires us to apply the definition of injective functions a few times! Remember a function is injective if any two distinct elements in its domain are mapped to distinct elements in the codomain. In other words, injective functions preserve distinctness. And in this lesson we'll prove that function composition preserves injectiveness!

Proof that composition of surjective functions is surjective:    • Proof: Composition of Surjective Func...  



I hope you find this video helpful, and be sure to ask any questions down in the comments!

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