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Chapter 11: Q. 6 (page 859)

Let y = f (x). State the definition for the continuity of the function f at a point c in the domain of f .

Short Answer

Expert verified

Thecontinuityordiscontinuityoffatapoint'c'canbesaidonlywhen'c'isinthedomainoff

Step by step solution

01

Step 1. Given information is:

A function y = f(x)

02

Step 2. Checking continuity of function f

Considery=f(x)Theobjectiveistodefinethecontinuityofthefunctionfatapointcinthedomainoff.Definition:Risthesetofrealnumbers.LetE鈯�R,f:E鈫�Randc鈭�E,thenwesaythatfiscontinuousatcisgiven蔚>0thereexistsa未>0suchthatf(x)-f(c)<蔚wheneverx鈭�Eandx-c<未.Iffisnotcontinuousatc,thenwesaythatfisdiscontinuousatc.Note:thecontinuityordiscontinuityoffatapoint'c'canbesaidonlywhen'c'isinthedomainoff.Forexample:Apolynomialfunctiondefinedbyf:R鈫�Randf(x)=-5x+10iscontinuousateverypointofR.

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