Q. 185.0( 2 Votes )

Find all points of discontinuity of the function where

Answer :

Given,



To find: Points discontinuity of function f(t) where t =


As t is not defined at x = 1 as denominator becomes 0,at x = 1.


x = 1 is a point of discontinuity


f(t) =


f(t) =


Clearly f(t) is not going to be defined whenever denominator is 0 and thus will give a point of discontinuity.


Solution of the following equation gives other points of discontinuities.


-2x2 + 5x – 2 = 0


2x2 – 5x + 2 = 0


2x2 – 4x – x + 2 = 0


2x(x – 2) – (x – 2) = 0


(2x – 1)(x – 2) = 0


x = 2 or x = 1/2


Hence,


f(t) is discontinuous at x = 1, x = 2 and x = 1/2


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