Question 1; (a) For the function f: [012], which is defined by the conditions. x, when 0

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.7: Inverse Functions
Problem 2SE: Why do we restrict the domain of the function f(x)=x2 to find the function's inverse?
Question

Please answer in 10 min

Question 1:
(a) For the function f: [012], which is defined
by the conditions
f(x).
x, when 0<x< 1
when x = 1
2
1
4-x, when 1<x<2
upper and lower sum when the interval is
divided into five equal parts.
(b) Prove that the function f: [012] → R is
Riemann integrable, when f(x) = 2x (without using
the knowledge that a monotonic function is
Riemann integrable).
(c) Define the function f: [0,1] → {0,1}
f(x) = { 1, when x + 141 +₂ 12/
other times.
Show the function to be Riemann integrable.
Transcribed Image Text:Question 1: (a) For the function f: [012], which is defined by the conditions f(x). x, when 0<x< 1 when x = 1 2 1 4-x, when 1<x<2 upper and lower sum when the interval is divided into five equal parts. (b) Prove that the function f: [012] → R is Riemann integrable, when f(x) = 2x (without using the knowledge that a monotonic function is Riemann integrable). (c) Define the function f: [0,1] → {0,1} f(x) = { 1, when x + 141 +₂ 12/ other times. Show the function to be Riemann integrable.
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