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Title: Composition of Maps
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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 7 | Composition of Maps
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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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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: sls07_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 $f: A \rightarrow B$ and $g: B \rightarrow C$ be two maps. What is correct for the composition $g \circ f$?
A1: It’s a map $g \circ f: A \rightarrow C$.
A2: It’s a map $g \circ f: A \rightarrow B$.
A3: It’s a map $g \circ f: B \rightarrow C$.
A4: It’s a map $g \circ f: C \rightarrow A$.
Q2: Let $f: A \rightarrow B$ and $g: B \rightarrow C$ be two maps. What is correct for the composition $g \circ f$?
A1: $(g \circ f)(x) = g(f(x))$.
A2: $(g \circ f)(x) = f(g(x))$.
A3: $(g \circ f)(x) = g(x) + f(x)$.
A4: $(g \circ f)(x) = g(x) \cdot f(x)$.
Q3: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ given by $f(x) = \cos(x)$ and $g(x) = x^5$. Which claim is not correct?
A1: $(g \circ f)(x) = \cos(x^5)$.
A2: $(f \circ g)(x) = \cos(x^5)$.
A3: $(g \circ f)(x) = \cos(x)^5$.
A4: One needs more information.
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Last update: 2025-09
