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Consider functions f and g such that com...

Consider functions f and g such that composite gof is defined and is one-one.Are f and g both necessarily one-one.

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To determine whether both functions \( f \) and \( g \) must be one-to-one (injective) given that their composition \( g \circ f \) is one-to-one, we can analyze the properties of these functions step by step. ### Step-by-Step Solution 1. **Understanding the Composition**: The composition of two functions \( g \) and \( f \), denoted as \( g \circ f \), means that for any element \( x \) in the domain of \( f \), \( g(f(x)) \) is defined. We are given that \( g \circ f \) is one-to-one. 2. **Definition of One-to-One Function**: ...
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