Home
Class 12
MATHS
Let f(x)=30-2x -x^3, the number ofthe po...

Let `f(x)=30-2x -x^3`, the number ofthe positive integral values of x which does satisfy `f(f(f(x)))) gt f(f(-x))` is

Text Solution

Verified by Experts

The correct Answer is:
2
`f(X)=30-2x-x^(3)`
`f(X)=-2-3xA^(2)lt0`
`rarr` f(X) is decreasing funciton
Henne `f(f(fx))gtf(f-x))`
`rarr f(f(x))ltf(-x)`
`rarr f(x)gt-x`
`rarr 30-2x-x^(3)gt-x`
`rarr x^(3)+x-30lt0`
`rarr(x-3)(x^(2)+3x+10)lt0`
`rarr xlt3`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise JEE Main Previous Year|10 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|17 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Matrix Match Type|12 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

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

Range ofthe function f(x)=cos(Ksin x) is [-1,1] , then the least positive integral value of K will be

The number of integers in the domain of function, satisfying f(x)+f(x^(-1))=(x^3+1)/x ,i s_____

The number of integers in the domain of function, satisfying f(x)+f(x^(-1))=(x^3+1)/x ,i s_____

Let f(x) = x-[x] , for every real number x, where [x] is integral part of x. Then int_(-1) ^1 f(x) dx is

Let f(x) = max. {|x^2 - 2| x ||,| x |} then number of points where f(x) is non derivable, is :

IF f(x) = ( x+2)/(3x-1) , then f(f(x)) is

Let f (x) be a quadratic expressinon which is positive for all real values of x, If g(x)=f(x)+f'(x)+f''(x), then for any real x

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

Let f :RtoR be a positive, increasing function with lim_(xtooo) (f(3x))/(f(x))=1 . Then lim_(xtooo) (f(2x))/(f(x)) is equal to

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Numerical)
  1. If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real...

    Text Solution

    |

  2. From a given solid cone of height H, another inverted cone is carved w...

    Text Solution

    |

  3. L e tf(x)={x^3+x^2+3x+sinx|(3+s in1/x ,),x!=0. 0x=0 then the number o...

    Text Solution

    |

  4. Leg f(x) be a cubic polynomial which has local maximum at x=-1a n df(x...

    Text Solution

    |

  5. consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1...

    Text Solution

    |

  6. If m is the minimum value of f(x , y)=x^2-4x+y^2+6y when xa n dy are s...

    Text Solution

    |

  7. For a cubic function y=f(x),f^(x)=4x at each point (x , y) on it and i...

    Text Solution

    |

  8. Number of integral values of b for which the equation (x^3)/3-x=b has ...

    Text Solution

    |

  9. L e tf(x)={x+2,x<-1x^2,-1lt=x<1(x-2)^2,xgeq1 Then number of times f^(...

    Text Solution

    |

  10. The number of nonzero integral values of a for which the function f(x)...

    Text Solution

    |

  11. L egf(x)={x^(3/5),ifxlt=1-(x-2)^3,ifx >1 Then the number of critical ...

    Text Solution

    |

  12. A right triangle is drawn in a semicircle of radius 1/2 with one of...

    Text Solution

    |

  13. A rectangle with one side lying along the x-axis is to be inscribed in...

    Text Solution

    |

  14. The least integral value of x where f(x)=(log)(1/2)(x^2-2x-3) is monot...

    Text Solution

    |

  15. The least area of a circle circumscribing any right triangle of area 9...

    Text Solution

    |

  16. L e tf(x)={|x^2-3x|+a ,0lt=x<3/2-2x+3,xgeq3/2 If f(x) has a local max...

    Text Solution

    |

  17. Let f(x)=30-2x -x^3, the number ofthe positive integral values of x wh...

    Text Solution

    |

  18. Let f(x) ={{:(x(x-1)(x-2),(0lexltn),sin(pix),(nlexle2n):} least valu...

    Text Solution

    |

  19. Number of critical point of the function f(X) =x+sqrt(|x|) is .

    Text Solution

    |

  20. consider f(X) =(1)/(1+|x|)+(1)/(1+|x-1|) Let x(1) and x(2) be point wh...

    Text Solution

    |