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10) Show that [x] = −[−x] A 11) suppose that g: A → B and f: BC, where A = B = C = {1,2,3,4}, g = {(1,4), (2, 1), (3, 1), (4, 2)}, and f = {(1,3), (2, 2), (3, 4), (4, 2)} . Find fog. Find go f. Find gog. Find go (gog).

10) Show that [x] = −[−x] A 11) suppose that g: A → B and f: BC, where A = B = C = {1,2,3,4}, g = {(1,4), (2, 1), (3, 1), (4, 2)}, and f = {(1,3), (2, 2), (3, 4), (4, 2)} . Find fog. Find go f. Find gog. Find go (gog).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 10:** Show that \(\lfloor x \rfloor = -\lceil -x \rceil\). **Problem 11:** Suppose that \(g: A \to B\) and \(f: B \to C\), where \(A = B = C = \{1, 2, 3, 4\}\), \(g = \{(1, 4), (2, 1), (3, 1), (4, 2)\}\), and \(f = \{(1, 3), (2, 2), (3, 4), (4, 2)\}\). 1. Find \(f \circ g\). 2. Find \(g \circ f\). 3. Find \(g \circ (g \circ g)\).
Transcribed Image Text:**Problem 10:** Show that \(\lfloor x \rfloor = -\lceil -x \rceil\). **Problem 11:** Suppose that \(g: A \to B\) and \(f: B \to C\), where \(A = B = C = \{1, 2, 3, 4\}\), \(g = \{(1, 4), (2, 1), (3, 1), (4, 2)\}\), and \(f = \{(1, 3), (2, 2), (3, 4), (4, 2)\}\). 1. Find \(f \circ g\). 2. Find \(g \circ f\). 3. Find \(g \circ (g \circ g)\).
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