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Problem 9. For each of the following functions d: RxR → [0, 0o), say whether d is a metric. Briefly explain your reasoning. a. d(x, y) = 2/x - yl b. d(x, y) = |x|+ lyl. bas c. d(x, y) = |I| 1+y* d. d(x, y) = x - y|³. teq ai Y. it seit vor, Auskios die tou a Z iw bigatxe i sviD.3 moldor

Problem 9. For each of the following functions d: RxR → [0, 0o), say whether d is a metric. Briefly explain your reasoning. a. d(x, y) = 2/x - yl b. d(x, y) = |x|+ lyl. bas c. d(x, y) = |I| 1+y* d. d(x, y) = x - y|³. teq ai Y. it seit vor, Auskios die tou a Z iw bigatxe i sviD.3 moldor

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 9 For each of the following functions \( d: \mathbb{R} \times \mathbb{R} \rightarrow [0, \infty) \), say whether \( d \) is a metric. Briefly explain your reasoning. a. \( d(x, y) = 2|x - y| \) b. \( d(x, y) = |x| + |y| \) c. \( d(x, y) = \frac{|x|}{1 + |y|} \) d. \( d(x, y) = |x - y|^{1/3} \)
Transcribed Image Text:## Problem 9 For each of the following functions \( d: \mathbb{R} \times \mathbb{R} \rightarrow [0, \infty) \), say whether \( d \) is a metric. Briefly explain your reasoning. a. \( d(x, y) = 2|x - y| \) b. \( d(x, y) = |x| + |y| \) c. \( d(x, y) = \frac{|x|}{1 + |y|} \) d. \( d(x, y) = |x - y|^{1/3} \)
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