It is known that there is a rational number between any two distinct irrational numbers. Consider a continuous function f : R → R such that f (x) = sin x for every rational number r. If x is an irrational number then, A. f(r) = sin(;)+ cos(;) B. f(x) = sinz + COSI C. f(x) Cos z = COS x D. f(x) = sin x
It is known that there is a rational number between any two distinct irrational numbers. Consider a continuous function f : R → R such that f (x) = sin x for every rational number r. If x is an irrational number then, A. f(r) = sin(;)+ cos(;) B. f(x) = sinz + COSI C. f(x) Cos z = COS x D. f(x) = sin x
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 53E
Related questions
Question
The question is attached in the image. The question is fairly simple please provide a proof as well as an intuition which could help to solve such problems quickly. Thank you.
(PS: how do i quickly realize that options other than,than f(x)= sinx, will not be continuous?)
Transcribed Image Text:36. It is known that there is a rational number between any two distinct irrational numbers.
Consider a continuous function f : R → R such that f(x)
= sin x for every rational
number x. If x is an irrational number then,
A. f(x) = sin(;) + cos(;)
B. f(x) = sinr + cos E
C. f(x) = cOS x
D. f(x) = sin x
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 5 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning