Let f ( x ) = ⎩ ⎨ ⎧ 3 x , min { 1 + x + [ x ] , x + 2 [ x ]} , 5 , x 2 , where [.] denotes greatest integer function. If α and β are the number of points, where f is not contin

Question

Let f ( x ) = ⎩ ⎨ ⎧ ​ 3 x , min { 1 + x + [ x ] , x + 2 [ x ]} , 5 , ​ x < 0 0 ≤ x ≤ 2 x > 2 , ​ where [.] denotes greatest integer function. If α and β are the number of points, where f is not continuous and is not differentiable, respectively, then α + β equals __________

TestHub · Accepted Answer

f ( x ) = ⎩ ⎨ ⎧ 3 x min { 1 + x , x } min { 2 + x , x + 2 } 5 ; ; ; ; x < 0 0 ≤ x < 1 1 ≤ x < 2 x > 2 f ( x ) = ⎩ ⎨ ⎧ 3 x x x + 2 5 ; ; ; ; x < 0 0 ≤ x < 1 1 ≤ x < 2 x > 2 Not continuous at x ∈ { 1 , 2 } ⇒ α = 2 Not diff. at x ∈ { 0 , 1 , 2 } ⇒ β = 3 α + β = 5

Mathematics - Continuity - Differentiability Question with Solution | TestHub

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