Mathematics:Teaching, Learning and Exploring.
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(Part B Question: NET June-2015) Let \(f: X \to X \) be such that \(f(x) = x \) for all \(x \in X \). Then
A. \(f \) is one-one and onto
B. \(f \) is one-one but not onto
C. \(f \) is onto but not one-one
D. \(f \) need not be either one-one or onto
\(\textbf{Option A}\)
\(f \) is onto as for \(x \in X \) there is \(y = f(x) \in X \) such that \(f(y) = x \). \(f \) is one -one as
\(f(x) = f(y) \implies f((f(x))=f(f(y)) \implies x=y \)
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