Prove that: f(x) = x(x-1) if x is rational = 0 if x is irrational is continuous at x = 0 and x =1 and discontinuous everywhere else Let f be a real-valued function whose domain is a subset of R. Then f is continuous at x_0 in dom(f) if and only if for each e > 0 there exists δ > 0 such that x ∈ dom(f) and |x − x_0| < δ imply |f(x) − f(x_0)| < e.

Prove that: f(x) = x(x-1) if x is rational = 0 if x is irrational is continuous at x = 0 and x =1 and discontinuous everywhere else Let f be a real-valued function whose domain is a subset of R. Then f is continuous at x_0 in dom(f) if and only if for each e > 0 there exists δ > 0 such that x ∈ dom(f) and |x − x_0| < δ imply |f(x) − f(x_0)| < e.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 53E

See similar textbooks