Home
Class 12
MATHS
If f(x)=-x^(3)-3x^(2)-2x+a,a in R then t...

If f(x)=`-x^(3)-3x^(2)-2x+a,a in R` then the real values of x satisfying `f(x^(2)+1)gtf(2x^(2)+2x+3)` will be

A

`(-oo,oo)`

B

`(0,oo)`

C

`-(oo,0)`

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
1
f(x)=`-3x^(2)=6x-2lt0 forall x gt 0`
So .,f(X) is decreasing for `x gtx`
Now `x^(2)+1,2x^(2)+2x+3gt0`
`therefore f(x^(2)+1)gtf(2x^(2)+2x+3)`
`rarr x^(2)+1lt2x^(2)+3`
`rarrx^(2)+2x +2 gt0`
`rarr x in R`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|40 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|42 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.7|5 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

if F(x)=x^2-2x+3 then the set of values of x satisfying f(x-1)=f(x+1)

(i) If f(x) = 3x^(4)- 5x^(2) + 7, " find " f(x-1) (ii) If f(x) = x^(2) - 3x + 4 , then find the values of x satisfying f(x) = f(2x+1)

If f(x)=(4-2x)/(2+3x+3x^(2)) then the values of x for which f'(x)=0 is

If f'(x)=3x^(2)+2x-4 and f(1)=3, then f(x)=

If f(x)=(4-2x)/(2+3x+3x^(2)) then the value of x for which f'(x)=0 is

If f (x) = x^(2) -2x + 3, then the value of x for which f (x) = f(x +1) is

If f(x)=x^(3)+2x , then find the value of f(3) .

If (x^(3)+x^(2)+x+1)/(x^(3)-x^(2)+x-1)=(x^(2)+x+1)/(x^(2)-x+1), then the number of real value of x satisfying are

if f(x)=(9/(log_2 (3-2x))-1)^(1/3) then the value of a which satisfies f^-1(2a-4)=1/2 is

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Single)
  1. If f(x)=(t+3x-x^2)/(x-4), where t is a parameter that has minimum and ...

    Text Solution

    |

  2. The least value of a for which the equation 4/(sinx)+1/(1-sinx)=a has ...

    Text Solution

    |

  3. If f(x)=-x^(3)-3x^(2)-2x+a,a in R then the real values of x satisfying...

    Text Solution

    |

  4. which of the following is the greatest?

    Text Solution

    |

  5. If the equation 4x^(3)+5x+k=0(k in R) has a negative real root then

    Text Solution

    |

  6. A tangent is drawn to the ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costhet...

    Text Solution

    |

  7. The largest term in the sequence an=(n^2)/(n^3+200) is given by (529)/...

    Text Solution

    |

  8. A factory D is to be connected by a road with a straight railway line ...

    Text Solution

    |

  9. The volume of the greatest cylinder which can be inscribed in a cone o...

    Text Solution

    |

  10. A rectangle of the greatest area is inscribed in a trapezium A B C D ,...

    Text Solution

    |

  11. A bell tent consists of a conical portion above a cylindrical portion ...

    Text Solution

    |

  12. A rectangle is inscribed in an equilateral triangle of side length 2a ...

    Text Solution

    |

  13. Tangents are drawn to x^2+y^2=16 from the point P(0, h)dot These tange...

    Text Solution

    |

  14. The largest area of the trapezium inscribed in a semi-circle or radius...

    Text Solution

    |

  15. In the formula angleA+angleB+angleC=180^(@), if angleA=90^(@) and angl...

    Text Solution

    |

  16. Two runner A and B start at the origin and run along positive x axis ,...

    Text Solution

    |

  17. The fuel charges for running a train are proportional to the square of...

    Text Solution

    |

  18. A cylindrical gas container is closed at the top and open at the ...

    Text Solution

    |

  19. Prove that the least perimeter of an isosceles triangle in which a cir...

    Text Solution

    |

  20. A given right cone has volume p , and the largest right circular cylin...

    Text Solution

    |