Answer to Question #34185 in Real Analysis for lia_pratiwi

Question #34185

Let X be a nonempty set and let f: X-> R have bounded ranges in r. if a element R. show that : sup {a + f(x): x element X} = a + sup {f(x): x element X} .Show that we also have inf {a+f(x) : x element X} = a+ inf {f(x): x element X}

Expert's answer

Download Answer

Learn more about our help with Assignments: Real Analysis

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. let s subsets r be nonempty. Prove that if a number u in R has the properties : (i) for every n elem
2. Show that the length of the curve y=log sec x between the points x=0 and x=π/3 is log (2+√3).
3. Please find the maximum and minimum values of the function f(x)=(100+x^2)^(1/2)-x over non-negative
4. Let ε>0 and δ>0 and a Є R. Show that Vε(a)nVδ(a) and Vε(a)UVδ(a) are γ neighborhoods o
5. let a1=a2=5 and an+1=an +6an-1 ,n>=2.show by induction that an=3n-(-2)n if n>=1.
6. prove that if a∫b f(x)dx exists as a proper integral ,then limx∫b f(t)dt=0. x→b-
7. Consider all monic polynomials f(x)=x^2+bx+c, where b and c are real numbers. What is the minimum va