Prove or solve the following statements: a. The function f :Z x Z ----> Z x Z defined by the formula f(m,n) = (5m + 4n,4m + 3n) is bijective. Find its inverse. b. Is the function T:P(Z) ----> P(Z) defined as T(X) = Xbar bijective? If so, find T^(-1) c. Given a function f: A ----> B and a subset Y is a subset of B, is f(f^(-1) (Y)) = Y always true? Prove or give a counterexample. d. Given f : A ------> B and subsets Y, Z are subsets of B, prove f^(-1) of (Y intersect Z) = f^(-1) of (Y) intersect f^(-1) of (Z).

Prove or solve the following statements: a. The function f :Z x Z ----> Z x Z defined by the formula f(m,n) = (5m + 4n,4m + 3n) is bijective. Find its inverse. b. Is the function T:P(Z) ----> P(Z) defined as T(X) = Xbar bijective? If so, find T^(-1) c. Given a function f: A ----> B and a subset Y is a subset of B, is f(f^(-1) (Y)) = Y always true? Prove or give a counterexample. d. Given f : A ------> B and subsets Y, Z are subsets of B, prove f^(-1) of (Y intersect Z) = f^(-1) of (Y) intersect f^(-1) of (Z).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 63RE

See similar textbooks

Similar questions

Show that the function fx)=ax is its own inverse for all real numbers a.
Find the cubic polynomial function f with real coefficients that has 1 and 2+i as zeros, and f2=2.
Find a fourth-degree polynomial function f with real coefficients that has 2, 2, and 7i as zeros.
Find all real zeros of fx=8x34x2+6x3.
Show that the function f(x)=3(x5)2+7 is not one-to-one.
Use Descartes Rule of Signs to find the number of possible positive, negative, and nonreal zeros of each function. P(x)=5x7+3x62x5+3x4+9x3+x2+1
Describe the end behavior of each polynomial. (a) y=x38x2+2x15 End behavior: y as x y as x (b) y=2x4+12x+100 End behavior: y as x y as x