JEE Main2013MathematicsContinuity and DifferentiabilityActual

Let f be a composite function of x defined by f(u)= 1 u^2+u-2 , u(x)= 1 x-1 . Then the number of points x where f is discontinuous is :

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Correct answer

B. 3

Step-by-step solution

(x)= 1 x-1 , which is discontinous at x=1 f(u)= 1 u^2+u-2 = 1 (u+2)(u-1) , which is discontinous at u=-2,1 when u=-2 , then 1 x-1 =-2 x= 1 2 when u=1 , then 1 x-1 =1 x=2 Hence given composite function is discontinous at three points, x=1, 1 2 and 2 .

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