Let f(x)= \{ \table 3 x{,} , x< 0; \min \{1+x[x], x+2[x]\}{,}, 0 \leq x \leq 2 ;5{,}, x>2 where [.] denotes greatest integer function. If \alpha and \beta are the number of points, where f is not continuous and is not differentiable, respectively, then \alpha+\beta equals ______ [28 Jan 2025 Shift 1]

Limits, Continuity and Differentiability Part 3

Section: Mathematics

Question : 31 of 69

Marks: +1, -0

Let ‌‌f(x)={

3x,	x<0
min{1+x[x],x+2[x]}‌,	0≤x≤2
5,	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 ______

[28 Jan 2025 Shift 1]

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3x	;‌x<0
min{1+x,‌x}	;‌0≤x<1
min{2+x,‌x+2}	;‌1≤x<2
5	;‌x>2

3x	;‌x<0
x	;‌0≤x<1
x+2	;‌1≤x<2
5	;‌x>2