RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 9. Continuity

Subject: Maths - Class 12th

Q. No. 19 of Exercise 9.2

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19

Find all point of discontinuity of the function where

Clearly,


is discontinuous at x = 1 as t is not defined at this point.


f(t) being a composition of function involving t, it is also discontinuous at x = 1



by observing f(t) we can say that f(t) is not defined at


t = – 2 and t = 1.


this will also contribute to discontinuity


Hence,



x – 1 = –1/2


x = 1 – 1/2


x = 1/2


also other point of discontinuity is obtained by :



x – 1 = 1


x = 2


Hence points at which f(t) is discontinuous are x = { 1/2,1,2}


At all other point it is continuous.


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