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Title: Range, Image and Preimage
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Series: Start Learning Sets
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Parent Series: Start Learning Mathematics
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Chapter: Sets and Maps
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YouTube-Title: Start Learning Sets 5 | Range, Image and Preimage
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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Ad-free video: Watch Vimeo video
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: sls05_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $f: A \rightarrow B$ be a map. What is the correct definition for the range of $f$, denoted by $\mathrm{Ran}(f)$?
A1: ${ x \in A \mid f(x) = x }$
A2: ${ y \in A \mid f(x) = y }$
A3: ${ y \in B \mid \exists x \in A \colon f(x) = y }$
A4: ${ x \in A \mid \exists y \in B \colon f(x) = y }$
A5: ${ x \in A \mid \forall y \in B \colon f(x) = y }$
Q2: Let $f: A \rightarrow B$ be a map and $\tilde{B} \subseteq B$. What is the correct definition for the preimage of $\tilde{B}$ under $f$, denoted by $f^{-1} [ \tilde{B}]$?
A1: ${ x \in A \mid f(x) \in \tilde{B} }$
A2: ${ x \in A \mid f(x) \in A }$
A3: ${ x \in \tilde{B} \mid f(x) \in A }$
A4: ${ x \in \tilde{B} \mid f(x) \notin A }$
Q3: Let $f: {1,2,3,4 } \rightarrow {1,2}$ be given by $$ f(x) = \begin{cases} 1 & \text{ if } x \text{ odd } \ 2 & \text{ if } x \text{ even } \end{cases}$$ What is the preimage of ${2}$ under $f$?
A1: ${2,4}$
A2: ${1,2,4}$
A3: ${2,3,4}$
A4: ${2}$
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Last update: 2025-09
