# Discrete Structure lecture_15

Apr 28th, 2015
Studypool Tutor
University of Phoenix
Course: Information Technologies
Price: \$5 USD

Tutor description

It includes all the details about the Discrete structure with examples.Step by step solution.

Word Count: 560
Showing Page: 1/7
DISCREAT STRUCTURELECTURE # 15INVERSE OFFUNCTIONKHAWAJA TARIQ MAHMOODLecture # 15INVERSE OF FUNCTIONSINVERSE FUNCTION:Suppose f : X Y is a bijective function. Then the inverse function f 1 : Y X is defined as: y Y , f 1 y x y f x That is, f 1 sends each element of Y back to the element of Xthat it came from under f .fx=f-1(y)f(x)=yf-1X=domain of fY=co-domain of fINVERSE FUNCTION FROM AN ARROW DIAGRAM:Let the bijection f : X Y be defined by the arrow diagram.fKhawaja Tariq Mahmood.1..62.7384.9XYPage 2Lecture # 15INVERSE OF FUNCTIONSThe inverse function f 1 : Y X is represented below by the arrow diagram.f-1.61.72.8394.INVERSE FUNCTION FROM A FORMULA:Let f : R R be defined by the formula f x 4 x 1 x R . Then f is bijective, therefore f 1exists. By definition of f 1 , f 1 y x f x yNow solvingf x yfor x 4x 1 y(by definition of f) 4x y 1 xHence, f 1 y y 14y 1is the inverse of f x 4 x 1 which defines f 1 : R R4Khawaja Tariq Mahmood.Page 3Lecture # 15INVERSE OF FUNCTIONSg-1g1..a2..b3..cXY.a1..b2..c3.YXINVERSEFUNCTIONRemark: Inverse of a function may not be a function.f-1f1.2.3.X.a.a.b.b.cd1.2..c3.d

## Review from student

Studypool Student
" awesome work thanks "

1825 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors