Question

Please, help; f, g are functions
f:A--> B
g: B--> C
show that if gof is injective, then f is injective.

Answer 1

My attempt:
gof : A --> C
let z in C , there exists unique x in A such that gof (x) = z

Answer 2

gof(x) = g(f(x) ) = z
x is unique--> f(x) is unique --> f is injective
but It sounds weak.

Answer 3

i would start by picking \(a_1, a_2\in A\) and then show if \(f(a_1)=f(a_2)\) then \(a_1=a_2\) as that is the definition of injective

Answer 4

Thank you, let me try.

Answer 5

ok it should take one very short line

Answer 6

Oh, yeah, It's easier,

Answer 7

Thank you so much

Answer 8

very
yw