Real analysis
Not what you're looking for?
Given a function f and a subset A of its domain, let f(A) represent the range of f over the set A; f(A)={f(x) : x belong to A}.
a-Let f(x)=x^2. If A=[0,2](the closed interval{x belong to R : 0<=x<=2}) and B=[1,4],find f(A) and f(B).Does f(A intersection B)=f(A) intersection f(B) in this case?.Does f(A U B)=f(A) U f(B)?.
b-Find two sets A and B for which f(A intersection B) does not = f(A) intersection f(B)
c-show that for an arbitrary function g:R-->R, it is always true that g(A intersection B) subset or equal g(A) intersection g(B) for all sets A,B subset or equal to R
d-Form and prove a conjecture about the relationship between g(A U B) and g(A) U g(B) for an arbitrary function g.
Purchase this Solution
Solution Summary
Topics involved in this solution set include intersections of sets (does f(A U B) = f(A) U f(B)?), and forming a conjecture regarding these intersections.
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
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.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.