Home
Class 12
MATHS
Let f : (-2,2) to RR be defined by f(x)=...

Let `f : (-2,2) to RR` be defined by
`f(x)={(x[x],"", -2ltxlt0),((x-1)[x],"",0lexle2):}`
where `[x]` denotes the greatest integer function. If `m and n` respectively are the number of points in `(-2, 2)` at which `y= abs(f (x))` is not continuous and not differentiable, then `m+n` is equal to _____

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2022

    JEE MAINS PREVIOUS YEAR|Exercise Question|454 Videos

  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos

Similar Questions

Explore conceptually related problems

f(x)=1/([abs(x-2}]+[abs(x-10)]-8) where [*] denotes the greatest integer function.

If f(x)=x+{-x}+[x] , where [x] and {x} denotes greatest integer function and fractional part function respectively, then find the number of points at which f(x) is both discontinuous and non-differentiable in [-2,2] .

f(x)=1+[cos x]x, in 0<=x<=(x)/(2) (where [.] denotes greatest integer function)

Given lim_(x to 0)(f(x))/(x^(2))=2 , where [.] denotes the greatest integer function, then

f(x)=1+[cos x]x in 0<=x<=(pi)/(2) (where [.] denotes greatest integer function)

If f(x)= {(|1-4x^2|,; 0 lt= x lt 1), ([x^2-2x],; 1 lt= x lt 2):} , where [.] denotes the greatest integer function, then f(x) is

Let f(x)=|2x^(2)+5|x|-3|,x in R .If "m" and "n" denote the number of points where "f" is not continuous and not differentiable respectively,then "m+n" is equal to:

JEE MAINS PREVIOUS YEAR-JEE MAIN 2023-Question
  1. Let y= p(x) be the parabola passing through the points (-1, 0), (0, 1)...

    Text Solution

    |

  2. Some couples participated in a mixed doubles badminton tournament. If ...

    Text Solution

    |

  3. Let f : (-2,2) to RR be defined by f(x)={(x[x],"", -2ltxlt0),((x-1)[x]...

    Text Solution

    |

  4. The sum of all these terms, of the arithmetic progression 3, 8, 13, . ...

    Text Solution

    |

  5. Let a, b, c be three distinct positive real numbers such that (2a)^(lo...

    Text Solution

    |

  6. Let a common tangent to the curves y^2=4x and (x-4)^2 +y^2 =16 touch t...

    Text Solution

    |

  7. If the mean of the frequency distribution is 28, then its varianc...

    Text Solution

    |

  8. The coefficient of x^7 in (1-x+2x^3)^10 is

    Text Solution

    |

  9. The distance of the point (-1,2,3) from the plane vecr*(hati-2hatj+hat...

    Text Solution

    |

  10. max(0lexlepi){x-2sinxcosx+1/3sin3x} =

    Text Solution

    |

  11. Among (S1) : lim(n to oo)1/(n^2)(2+4+6+.......+2n)=1 (S2) : lim (n...

    Text Solution

    |

  12. Let B=[[1,3,a],[1,2,3],[a,a,4]] , a gt 2 be the adjoint of a matrix A ...

    Text Solution

    |

  13. Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatk and vecc =2hati-hatj+...

    Text Solution

    |

  14. The set of all a in RR for which the equation x|x-1|+|x+2|+a=0 has exa...

    Text Solution

    |

  15. A coin is biased so that head is 3 times as likely to occur as tail. t...

    Text Solution

    |

  16. Let PQ be a focal chord of the parabola y^2=36x of lenght 100, making ...

    Text Solution

    |

  17. The area of the region enclosed by the curve f(x)=max{sinx,cosx},-pile...

    Text Solution

    |

  18. The number of symmetric matrices of order 3, with all the entries from...

    Text Solution

    |

  19. Fractional part of the number (4^(2022))/(15) is equal to

    Text Solution

    |

  20. Let s1,s2,s3,......,s(10) and the common differences are 1,3,5,.....,1...

    Text Solution

    |