Are f and g both necessarily onto, if gof is onto?
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Solution Consider f : {1, 2, 3, 4} → {1, 2, 3, 4} and g : {1, 2, 3, 4} → {1, 2, 3} definedas f(1) = 1, f(2) = 2, f(3) = f(4) = 3, g (1) = 1, g (2) = 2 and g (3) = g (4) = 3. It can beseen that gof is onto but f is not onto.
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