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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%7

Number of points of discontinuity of \mathrm{f(x)=\left[\sin ^{-1} x\right]-[x]} in its domain is equal to (where [.] denots 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]

\left.\mid \sin ^{-1} t\right] is discontinuous at x=-sin 1,0,sin 1

[x] is dicountinuous at x=0,1

Now 

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

Hence f(x) is continuous at x=0

Therefore points of discountinuityare -\sin 1, \sin 1 \text { and } 1 \text {. }

Posted by

seema garhwal

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