3. ** Prove that the relation D given by xDy iff / EZ ΕΖ (namely, xDy if x is a divisor of y), on the set Z is reflexive and transitive.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3. *** Prove that the relation D given by
xDy iff / EZ
X
(namely, xDy if x is a divisor of y), on the set Z is reflexive and transitive.
3
4. ** Prove the function f : R − {1} → R - {1} defined by ƒ(x) = (±)³ is bijective.
5. ** Consider the functions f: Rx RR and g: RRxR given by
f(x, y) = x - y andg(x) = (x,x²)
Find the formulas for fog and go f.
6. * The function f : R → (0, +∞) given by f(x) = e³+¹ is bijective. Find its inverse.
Transcribed Image Text:3. *** Prove that the relation D given by xDy iff / EZ X (namely, xDy if x is a divisor of y), on the set Z is reflexive and transitive. 3 4. ** Prove the function f : R − {1} → R - {1} defined by ƒ(x) = (±)³ is bijective. 5. ** Consider the functions f: Rx RR and g: RRxR given by f(x, y) = x - y andg(x) = (x,x²) Find the formulas for fog and go f. 6. * The function f : R → (0, +∞) given by f(x) = e³+¹ is bijective. Find its inverse.
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