   Chapter 2.5, Problem 54E

Chapter
Section
Textbook Problem

In Exercises 45-56, find the values of x for which each function is continuous.54. f ( x ) = { − 2 x + 1 if  x < 0 x 2 + 1 if  x ≥ 0

To determine
The value of x at which the function is continuous.

Explanation

Given information:

The function is f(x)={2x+1ifx<0x2+1ifx0

Definition used:

A function f is continuous at x=a when it follows the following three conditions,

(1) f(a) is defined.

(2) limxaf(x) exists.

(3) limxaf(x)=f(a) .

Calculation:

For the function to be continuous, it should satisfy all the three conditions.

For x<0 , the value of left hand limit is,

limx0f(x)=limx0(2x+1)=20+1=1

For x>0 , the value of right hand limit is,

limx

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