Q. 193.7( 3 Votes )

Find all point of discontinuity of the function where

Answer :

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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