Let [ x ] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f ( x ) = [ x ] + ∣ x − 2∣ , − 2

Question

Let [ x ] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f ( x ) = [ x ] + ∣ x − 2∣ , − 2 < x < 3 , is not continuous and not differentiable. Then m + n is equal to :

TestHub · Accepted Answer

​ f ( x ) = [ x ] + ∣ x − 2∣ , − 2 < x < 3 ∴ f ( x ) = ⎩ ⎨ ⎧ ​ − x , − 2 < x < − 1 1 − x , − 1 ≤ x < 0 2 − x , 0 ≤ x < 1 3 − x , 1 ≤ x < 2 x , 2 ≤ x < 3 ​ ​ It is clearly discontinues at 4 points and nondifferentiable at 4 points. ∴ m + n = 8

Mathematics - Continuity - Differentiability Question with Solution | TestHub

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