Home
Class 12
MATHS
Number of points of discontinuity of f(x...

Number of points of discontinuity of `f(x)=[sin^(-1)x]-[x]` in its domain is equal to (where [.] denotes the greatest integer function) a. 0 b. 1`` c. 2 d. 3

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
Domain of the function is `[-1,1]`
`[sin^(-1)x]` is discontinuous at `x=-sin1,0, sin 1`
[x] is discontinuous at x = 0,1
Now `f(0^(+))=[0^(+)]-[0^(+)]=0-0=0`
`f(0^(-))=[0^(-)]-[0^(-)]=-1-(-1)=0`
Hence f(x) is continuous at x = 0.
Therefore points of discontinuity are `-sin 1, sin 1 and 1.`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

lim_(xrarr1([x]+[x]) , (where [.] denotes the greatest integer function )

If f(x)= [sin^2x] (where [.] denotes the greatest integer function ) then :

Period of f(x) = sgn([x] +[-x]) is equal to (where [.] denotes greatest integer function

Domain of f(x)=sin^-1[2-4x^2] is ([.] denotes the greatest integer function)

Solve lim_(xrarr1)[sin^(-1)x] (where [.] denotes greatest integer function.)

underset(xrarr0)(lim)[(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the greatest integer function)

Solve [cot^(-1) x] + [cos^(-1) x] =0 , where [.] denotes the greatest integer function

Statement 1: Minimum number of points of discontinuity of the function f(x)=(g(x)[2x-1]AAx in (-3,-1) , where [.] denotes the greatest integer function. and g(x)=a x^3+x^2+1 is zero. Statement 2: f(x) can be continuous at a point of discontinuity, say x=c_1 of [2x-1] if g(c_1)=0. which statement is true?

If f(x)=cos |x|+[|sin x/2|] (where [.] denotes the greatest integer function), then f (x) is

The value of int_0^1.5 [x^2] dx is : where [x] denotes greatest integer function.

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

    Text Solution

    |

  2. Let f(x)=[t a n x[cot x]],x [pi/(12),pi/(12)] , (where [.] denotes the...

    Text Solution

    |

  3. Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domai...

    Text Solution

    |

  4. If g(x)=(lim)(mvecoo)(x^mf(x)+h(x)+3)/(2x^m+4x+1) when x!=1a n dg(1)=e...

    Text Solution

    |

  5. The number of points of discontinuity of fx)=[2x^2]-{2x2}^2 (where [] ...

    Text Solution

    |

  6. If f(x)={(|x|-3 when x < 1), and (|x-2|+a , when x >= 1) & g(x)={2...

    Text Solution

    |

  7. The function f(x)=(x^3)/8-s inpix+4in[-4,4] does not take the value -4...

    Text Solution

    |

  8. Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-...

    Text Solution

    |

  9. Let f(x)={{:(x[(1)/(x)]+x[x],if, x ne0),(0,if,x=0):} (where [x] denote...

    Text Solution

    |

  10. A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...

    Text Solution

    |

  11. If is an even function such that lim(h rarr 0) (f(h)-f(0))/(h) has som...

    Text Solution

    |

  12. Number of point where function f(x) defined as f:[0,2pi] rarrR,f(x)={{...

    Text Solution

    |

  13. If y=e^x sinx, then find dy/dx

    Text Solution

    |

  14. If y=cos(sin^(-1)x), then find dy/dx

    Text Solution

    |

  15. If y=sina^x, then find dy/dx

    Text Solution

    |

  16. If y=1/(1 + 1/x), then find dy/dx

    Text Solution

    |

  17. If y=cos(x^3), then find dy/dx

    Text Solution

    |

  18. If y=(1-x)tan(x/2), then find dy/dx

    Text Solution

    |

  19. If y=1/(1+x^3), then find dy/dx

    Text Solution

    |

  20. If y=sin(x^2-3x), then find dy/dx

    Text Solution

    |