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  • Number of points of discontinuity of <img alt="\mathrm{f(x)=\left[\sin ^{-1} x\right]-[x]}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%5Cleft%5B%5Csin%20%5E%7B-1%7

Number of points of discontinuity of \mathrm{f(x)=\left[\sin ^{-1} x\right]-[x]}  in its domain is equal to (where \mathrm{[\cdot]} denotes the greatest integer function)

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

3


Answers (1)

best_answer

Domain of the function is [-1,1]
\mathrm{\left[\sin ^{-1} x\right]}  is discontinuous at \mathrm{x=-\sin 1,0, \sin 1}
\mathrm{[x]}  is discontinuous at \mathrm{x=-\sin 1,0, \sin 1}
\mathrm{[x]} is discontinuous at \mathrm{x=0,1}

Now
\mathrm{f\left(0^{+}\right)=\left[0^{+}\right]-\left[0^{+}\right]=0-0=0}
\mathrm{f\left(0^{-}\right)=\left[0^{-}\right]-\left[0^{-}\right]=-1-(-1)=0}

Hence \mathrm{f(x)} is continuous at \mathrm{x=0}.

Therefore points of discontinuity are \mathrm{-\sin 1, \sin 1\: and \: 1 .}

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manish

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