Home
Class 12
MATHS
For the real number x, let f (x)=(1)/( "...

For the real number x, let `f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))).` Find the number of real roots of the equation
`f(f (.....(f(x)).....)= ({-x}`
where f is applies 2013 times and {.} denotes fractional part function.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise MATCHING TYPE PROBLEMS|6 Videos

  • ELLIPSE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

Find the number of real roots of the equation f(x) =x^(3) + 2x^(2) +x +2 =0

Let f (x) = x^(2)+10x+20. Find the number of real solution of the equation f (f (f (f(x))))=0

Let f (x)= x^3 -3x+1. Find the number of different real solution of the equation f (f(x) =0

If f(x)=2 for all real numbers x, then f(x+2)=

Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

f(x)=sqrt((x-1)/(x-2{x})) , where {*} denotes the fractional part.

The range of the function f(x) = frac{1-{x}}{1+{x}} is (where {.} denotes the fractional part of x )

Write the domain of the real function f(x)=1/(sqrt(|x|-x))

Find the domain and the range of the real function f defined by f(x)=sqrt((x-1)) .

Find the domain and the range of the real function f defined by f(x)=sqrt((x-1)) .

VIKAS GUPTA (BLACK BOOK) ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

    Text Solution

    |

  2. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

    Text Solution

    |

  3. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

    Text Solution

    |

  4. Find the number of elements contained in the range of the function f (...

    Text Solution

    |

  5. Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -...

    Text Solution

    |

  6. Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral va...

    Text Solution

    |

  7. The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...

    Text Solution

    |

  8. Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=...

    Text Solution

    |

  9. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  10. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  11. Let f(x)= cx+d/ax+b ​ . Then fof(x) = x provided that.

    Text Solution

    |

  12. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

    Text Solution

    |

  13. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  14. If f(x) is an even function then find the number of distinct real numb...

    Text Solution

    |

  15. The least integral value of m, m inR for which the range of function ...

    Text Solution

    |

  16. Let x1, x2, x3 satisfying the equation x^3 - x^2 + betax + gamma = 0 ...

    Text Solution

    |

  17. Let A={1,2,3,4}and B={0,1,2,3,4,5}. If 'm' is the number of strictly i...

    Text Solution

    |

  18. The value of sum(r=1)^1024 [log2 r] is equal to, ([.] denotes the gre...

    Text Solution

    |

  19. Let f (x) = (ax+b)/(xc+d), where a,b,c d are non zero If f (7) =7,f (1...

    Text Solution

    |

  20. It is pouring down rain and the amount of rain hitting point (x,y) is ...

    Text Solution

    |