simple Pure Mathematics proofs: left and right inverse of composite functions help?

March 1st, 2010 | by admin |

Let f : A -> B and g : B -> C be two functions.
a) Prove that if g ○ f has a left inverse, then f has a left inverse.
b) Prove that if g ○ f has a right inverse, then g has a right inverse.

I have spent about 4 total hours just manipulating the properties of these functions, and I can not come to a conclusion. I realize that these are probably very simple, but I am effectively stumped. Can anyone help?

consider that if w is the left inverse of [ g o f] then w o [ g o f ] = [w o g ] o f = identity

  1. One Response to “simple Pure Mathematics proofs: left and right inverse of composite functions help?”

  2. By ted s on Mar 1, 2010 | Reply

    consider that if w is the left inverse of [ g o f] then w o [ g o f ] = [w o g ] o f = identity
    References :

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