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Chapter 14: Q. 15 (page 905)

In Problem, determine whether f is continuous at c

fx=x2-4x+2,x鈮�-2-4,x=-2,c=-2

Short Answer

Expert verified

The given polynomial functionfx=x2-4x+2,x鈮�-2-4,x=-2,c=-2
is continuous

Step by step solution

01

Step1. Given information 

Polynomial functionfx=x2-4x+2,x鈮�-2-4,x=-2,c=-2

c=-2

We know that

A function is called continuous function when at x= a,

limx鈫�afx=fa

and defined for every number of domain

and

f(xx鈫�c)=Aandf(c)=A

02

Step2. Calculations of continuity 

Assume that x=-2 is in the domain of the given function, so we can proceed to find the continuity, for continuity x is the approach to -2,

so according to question

fx=x2-4x+2f(x)=x+2x-2x+2fx=x-2fxx鈫�-2=-2-2=-4

f(-2)=f(x)x鈫�-2

so the given function is continuous at x =-2

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