Show that fis continuous on (-00, ∞). 1-xifxs1 Rx) = {1-12 In(x) if x > 1 On the interval (-00, 1), fis-Select- function; therefore fis continuous on (-00, 1). On the interval (1, 0), fis-Select--- function; therefore f is continuous on (1, 0). At x=1, lim f(x) = lim X-17 and lim f(x) = lim x-1+ so lim f(x) = x-1+ Also, (1) Thus, fis continuous at x = 1. We conclude that fis continuous on (-co, co).
Show that fis continuous on (-00, ∞). 1-xifxs1 Rx) = {1-12 In(x) if x > 1 On the interval (-00, 1), fis-Select- function; therefore fis continuous on (-00, 1). On the interval (1, 0), fis-Select--- function; therefore f is continuous on (1, 0). At x=1, lim f(x) = lim X-17 and lim f(x) = lim x-1+ so lim f(x) = x-1+ Also, (1) Thus, fis continuous at x = 1. We conclude that fis continuous on (-co, co).
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.2: Polynomial Functions
Problem 96E: What is the purpose of the Intermediate Value Theorem?
Question
Transcribed Image Text:Show that fis continuous on (-00, ∞).
1-xifxs1
Rx) = {1-12
In(x)
if x > 1
On the interval (-00, 1), fis-Select-
function; therefore fis continuous on (-00, 1).
On the interval (1, 0), fis-Select---
function; therefore f is continuous on (1, 0).
At x=1,
lim f(x) = lim
X-17
and
lim f(x) = lim
x-1+
so lim f(x) =
x-1+
Also, (1)
Thus, fis continuous at x = 1. We conclude that fis continuous on (-co, co).
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