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Let $f \: \circ \: g$ denote function composition such that $(f \circ g)(x) = f(g(x))$. Let $f: A \rightarrow B$ such that for all $g \: : \: B \rightarrow A$ and $h \: : \: B \rightarrow A$ we have $f \: \circ \: g = f \: \circ \: h \: \Rightarrow g = h$. Which of the following must be true?

  1. $f$ is onto (surjective)
  2. $f$ is one-to-one (injective)
  3. $f$ is both one-to-one and onto (bijective)
  4. the range of $f$ is finite
  5. the domain of $f$ is finite

https://gateoverflow.in/95289/tifr2017-a-11


i'm not able to understand why f should be one-to-one 

asked in Set Theory & Algebra by Boss (34.6k points) | 21 views

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