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Composite function

  • Thread starter nikie1o2
  • Start date
  • #1
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Homework Statement


let A,B,C be sets, and let f : A--> B and g : B--> C be functions. The composite function denoted by g o f is a function from A to C defined as follows:



Homework Equations



g o f(x)=g(f(x)) for every x in A.

Prove that if g o f is one-to one, then f is one-to one
Prove that is g o f is onto, then g is onto

The Attempt at a Solution


I really don't know how to approach this problem. I didnt things similar with binary structures determining if they are an isomorphism by not familiar with composite functions
 

Answers and Replies

  • #2
23
0
I think I know how to approach it....check me if I'm right though

check if its one-to-one and onto

if it is one-to-one that implies if f(a)=f(b) then a=b
 

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