Explore BrainMass

Explore BrainMass

    Operations of Functions : Injective, Surjective and Bijective

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let f: A ?> B and g: B ?> C be functions.
    a) Suppose that f and g are injective. Show that g o f is injective.
    b) Suppose that f and g are surjective. Show that g o f is surjective.
    c) Suppose that f and g are bijective. Then g o f is bijective by parts a) and b). Show that (gof)^-1 = f^-1 o g^-1.

    Please do number 3 in attachment.

    Please see the attached file for the fully formatted problems.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:32 pm ad1c9bdddf


    Solution Summary

    Pointwise Operations ( Composition and Inverse ) of Injective, Surjective and Bijective Functions are investigated. The solution is detailed and well presented.