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
" Wow this is really good.... didn't expect it. Sweet!!!! "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1822 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