Proof about Functions
Not what you're looking for?
Let f: X-->Y be a function from one set X to another set Y, let S be a subset of X, and let U be a subset of Y. What in general can one say about f^-1(f(S)) and S? What about f(f^-1(U)) and U?
Purchase this Solution
Solution Summary
This solution explains how to provide proof for the given functions.
Solution Preview
Dear Student
Please find the attachment for the solutions.
Let f: X-->Y be a function from one set X to another set Y, let S be a subset of X, and let U be a subset of Y. What in general can one say about and f^-1(f(S)) and S? What about f(f^-1(U)) and U?
We know that f(S) denotes the set of the images of all elements of S under the function f.
So, f(s) = {b element of Y/ f(a) = b, for some a element of S}
Similarly f^-1(b) = {a element of S/f(a) = b, b element of Y} indicates the set of all elements of S that are mapped to some element b in Y through f.
Let us see two examples ...
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability