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Are f and g both necessarily onto, if go...

Are f and g both necessarily onto, if `gof`is onto?

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To determine whether both functions \( f \) and \( g \) must be onto if the composition \( g \circ f \) is onto, we can analyze the definitions and properties of onto functions. ### Step-by-Step Solution: 1. **Understanding Onto Functions**: A function \( f: A \to B \) is called onto (or surjective) if for every element \( b \) in the codomain \( B \), there exists at least one element \( a \) in the domain \( A \) such that \( f(a) = b \). 2. **Composition of Functions**: ...
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