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    Function Terminology of 'Onto' and 'One to One'

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    Assume f:A->B and g:B->C.
    a) Show that if f and g are both onto, then g o f is onto
    b) Show that if g o f is one-to-one, then f is one-to-one
    c) Show that if g o f is onto and g is one-to-one, then f is onto

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    Solution Preview

    Assume f:A->B and g:B->C.
    a) Show that if f and g are both onto, then g o f is onto
    Let x, y, z be any elements of A, B and C respectively.
    Since f is onto,
    Since g is onto,
    (g o f)(x) = g(f(x)) = g(y) = ...

    Solution Summary

    The expert examines function terminology of Onto and One to One.

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