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the unit circle S¹ = {(x, y) = R² ; x² + y² = 1} homeomorphic to the sequare T = {(x, y) = R² ; [x]+|y| = 1} here f: S¹ →T is de find by f(x, y) = [jxl+lyl + 1xl+lyl, y show that how we obtain the inverse to be: y X ( ( ₁² + y²) ¹2 + (x² + y2²)³ 1/2 f-¹ =

the unit circle S¹ = {(x, y) = R² ; x² + y² = 1} homeomorphic to the sequare T = {(x, y) = R² ; [x]+|y| = 1} here f: S¹ →T is de find by f(x, y) = [jxl+lyl + 1xl+lyl, y show that how we obtain the inverse to be: y X ( ( ₁² + y²) ¹2 + (x² + y2²)³ 1/2 f-¹ =

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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the unit circle S¹ = {(x, y) = R² ; x² + y² = 1} homeomorphic to the sequare T = {(x, y) = R²; [x|+|y| = 1} here f: S¹ →T is defind by f(x, y) = [(x+lyl + 1xl+lyl, y show that how we obtain the inverse to be: f-¹ y + (x² + y²) ¹/2² (x² + y²) ¹/2 (+² +1²) ¹2)
Transcribed Image Text:the unit circle S¹ = {(x, y) = R² ; x² + y² = 1} homeomorphic to the sequare T = {(x, y) = R²; [x|+|y| = 1} here f: S¹ →T is defind by f(x, y) = [(x+lyl + 1xl+lyl, y show that how we obtain the inverse to be: f-¹ y + (x² + y²) ¹/2² (x² + y²) ¹/2 (+² +1²) ¹2)
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