1. Determine whether or not the following relations are functions. If the given relation is a function, identify the domain and range of the function, and determine further whether or not the function is one-to-one. If the function is one-to-one, find its inverse, and use your answer to verify Theorem 2 (Inverse Functions). Show complete solutions. If the given relation is not a function or if the function is not one-to-one, show a contradiction. 13. y = |x| 14. I 15. y = : 1, where x > 0 = [ { x + ² if x ≥ 3 |-(4x+8)² ifx < − 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Determine whether or not the following relations are functions. If the given relation is a
function, identify the domain and range of the function, and determine further whether or not
the function is one-to-one. If the function is one-to-one, find its inverse, and use your answer
to verify Theorem 2 (Inverse Functions). Show complete solutions. If the given relation is not a
function or if the function is not one-to-one, show a contradiction.
13. y = |x|
14.
15. y =
= 1, where x ≥ 0
if x ≥ 3
√ √ ² x + ²/²
|-(4x+8)² if x < −3
Transcribed Image Text:1. Determine whether or not the following relations are functions. If the given relation is a function, identify the domain and range of the function, and determine further whether or not the function is one-to-one. If the function is one-to-one, find its inverse, and use your answer to verify Theorem 2 (Inverse Functions). Show complete solutions. If the given relation is not a function or if the function is not one-to-one, show a contradiction. 13. y = |x| 14. 15. y = = 1, where x ≥ 0 if x ≥ 3 √ √ ² x + ²/² |-(4x+8)² if x < −3
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