Question

Prove that if f : A → B, g : B → C, and g ◦ f is injective , then f : A injective

Answer 1

Check it down.

Explanation:

Injective functions or One to one functions are functions in each one element of A set is is mapped to another element of B set

1) Let's start by listing supposition and their respective Reasons

Suppose:

`g\circ f` is injective then
`f:A\rightarrow B` is also injective.

Reason: Given

2) Since we are dealing with injective (one to one) functions, we can rightly proceed:

`f(x)=f(y) \:such \:as\: x,y \in A`

`g(f(x))=g(f(y))`

Given the fact that
`g\circ f`

`x=y`

Then we can say that since
`g\circ f` f: A is an injective too ("one to one" ) function.