Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

If f(x)= x+ x +[x- x]+[x] where [y] and y denote greatest integer function and fractional part function of y respectively, then find the number of points of discontinuity in [0, ] .

Correct answer

Step-by-step solution

aligned f(x) & =x+ x-[x+ x]+[x- x]+[x] x+ x & =0,1,2,3 x=0, ₁, ₂, ₃ x- x & =0,1,2,3 x=0, ₁, ₂, ₃ aligned f is continuous at x=0 , but discontinuous at ₁, ₂, ₃, ₁, ₂, ₃, 1,2,3 Number of points of discontinuity =9 .

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