Home
Class 12
MATHS
Number of points where the function f(...

Number of points where the function
`f(x)={(1+["cos"(pix)/2],1ltxle2),(1-{x},0lexlt1),(|sinpix|,-1lexlt0):}`
and `f(1)=0` is continuous but non differentiable :
(where [.] denotes greatest integer function and {.} denotes fractional part function)

A

`1`

B

`2`

C

`3`

D

`0`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Consider the function f(x) = {x+2} [cos 2x] (where [.] denotes greatest integer function & {.} denotes fractional part function.)

f(x) = [x-1] + {x)^{x}, x in (1,3), then f^-1(x) is- (where [.] denotes greatest integer function and (J denotes fractional part function)

Solve (1)/(x)+(1)/([2x])={x}+(1)/(3) where [.] denotes the greatest integers function and {.} denotes fractional part function.

The function f(x)={x} sin (pi[x]) , where [.] denotes the greatest integer function and {.} is the fractional part function, is discontinuous at

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then

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

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

Number of points of discontinuity of f(x)={(x)/(5)}+{(x)/(2)} in x in[0,100] is/are (where [-] denotes greatest integer function and {:} denotes fractional part function)

ALLEN-TEST PAPERS-MATHEMATICS
  1. If y=f((2x-1)/(x^(2)+1)) and f^'(x)=sinx^(2), then (dy)/(dx) is equal ...

    Text Solution

    |

  2. f:RtoR such that f(2)=5 and f'(2)=10 thenlim(xto0) ((f(2+x))/(f(2)))^(...

    Text Solution

    |

  3. The value of lim(xto0^(+))(x^(x)+(tanx)^(cosecx)+(cosecx)^(tanx)) is...

    Text Solution

    |

  4. f:RtoR is defined as f(x)=x^(3)+2x^(2)+7x+cos(pix) and g be the invers...

    Text Solution

    |

  5. Let f(x) be a cubic polynomical such that f'(x)=0 at x=1 and x=3, f(1)...

    Text Solution

    |

  6. lim(xto oo)(ln(x^(2)+5x)-2ln(cx+1)=-2 then

    Text Solution

    |

  7. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  8. If quadratic equation (1+m)x^(2)-2(1+3m)x-2(1+m)=0 has one root greate...

    Text Solution

    |

  9. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

  10. Domain off(x)=log(x^2+5x+6)/([x]-1)where [.] denotes greatest integer ...

    Text Solution

    |

  11. Let f:RtoR f(x)=x+3x^(3)+5x^(5)+………..+1001x^(1001) then which of fol...

    Text Solution

    |

  12. The vaue of x satisfying sin^(-1)(x)+sin^(-1)(sqrt(15)x)=(pi)/2 is

    Text Solution

    |

  13. The sum sum(n=1)^oo tan^(-1)(3/(n^2+n-1)) is equal to

    Text Solution

    |

  14. Range of f(x)=sin^(-1)x+tan^(-1)x+sqrt(x+1) is [a,b] then b+a is equal...

    Text Solution

    |

  15. Let f(x)={(cos[x],xge0),(|x|+a,xlt0):} (where [.] denotes greatest i...

    Text Solution

    |

  16. lim(nto oo) (1-1/(2^(2)))(1-1/(3^(2)))(1-1/(4^(2)))…………….(1-1/(n^(2)))...

    Text Solution

    |

  17. The velue of lim(x->0)(sin(3sqrtx)ln(1+3x))/((tan^(- 1)sqrt(x))^2(e^(...

    Text Solution

    |

  18. Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...

    Text Solution

    |

  19. Let h (x) = min (x, x^2), x in R, then h (x) is

    Text Solution

    |

  20. Number of points where the function f(x)={(1+["cos"(pix)/2],1ltxle2)...

    Text Solution

    |