Answered: x² + 1, if x < 0 71. f(x) = %3D 1-x, if…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter11: Rational And Irrational Numbers

Section: Chapter Questions

Problem 23CLR

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74) Describe the intervals on which each function of f is continuous, and each point f fails to be continuous, use limits to determine type of discontinuity, and any left or right continuities.

x² + 1, if x < 0
71. f(x) =
%3D
1-x, if x >0

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$f (x) = \{\begin{cases} x^{2} + 1 i f x \leq 0 \\ 1 - x i f x \geq 0 \end{cases}$

$f (0) = 0 + 1 = 1$

$\lim_{x \to 0^{-}} = \lim_{x \to 0} (x^{2} + 1) \lim_{x \to 0^{-}} = 0 + 1 = 1$

Also,

$\lim_{x \to 0^{+}} = \lim_{x \to 0} (1 - x) \lim_{x \to 0^{+}} = 1 - 0 = 1$

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