Home
Class 12
MATHS
If x is real, then the value of the expr...

If `x` is real, then the value of the expression `(x^2+14 x+9)/(x^2+2x+3)` lies between (a) 5 and 4 (b) 5 and `-4` (c) `-5a n d4` (d) none of these

A

[4, 5]

B

[-4, 5]

C

[-5, 4]

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(x^(2)+14x+9)/(x^(2)+2x+3)=y`
or ` x^(2)+14x+9=x^(2)y+2xy+3y`
or ` x^(2)(y-1)+2x(y-7)+(3y-9)=0`
Since x is real, we have
`4(y-7)^(2)-4(3y-9)(y-1) ge 0`
or ` 4(y^(2)+49-14y)-4(3y^(2)+9-12y) ge 0`
or ` (y+5)(y-4) le 0`
` :. y in [-5,4]`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If x is real, then the value of the expression (x^2+14x+9)/(x^2+2x+3) lies between (a) 5 and 4 (b) 5 and -4 (c) -5 and 4 (d) none of these

If x is real, then x//(x^2-5x+9) =y lies between -1a n d-1//11 b. 1a n d-1//11 c. 1a n d1//11 d. none of these

Find the maximum value of (7−x)^4 (2+x)^5 when x lies between −2 and 7.

The value of expression x^4-8x^3+18 x^2-8x+2 when x=2+sqrt(3) a. 2 b. 1 c. 0 d. 3

The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=-sqrt(3) is 4 (b) 5 (c) 6 (d) none of these

If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre lies at the origin, and the centroid on the line x+y=7 , then the third vertex lies at (a) (7,4) (b) (8,14) (c) (12 ,21) (d) none of these

If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a. 3 b. no least value c. 0 d. none of these

The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a. 1 b. no least value c. 0 d. none of these

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. The number of integral values of x for which the function sqrt(sinx+co...

    Text Solution

    |

  2. 29. Which one of following best represents the graph of y=x^(logx pi)

    Text Solution

    |

  3. If x is real, then the value of the expression (x^2+14 x+9)/(x^2+2x+3)...

    Text Solution

    |

  4. The range of the function f(x)=|x-1|+|x-2|, -1 le x le 3, is

    Text Solution

    |

  5. The function f: R-R is defined by f(x)=cos^2x+sin^4xforx in Rdot Then...

    Text Solution

    |

  6. The range of f9x)=[|s in x|+|cosx"|""]"dot Where [.] denotes the great...

    Text Solution

    |

  7. The range of function f(x)=^(7-x)P(x-3)i s {1,2,3} (b) {1,2,3,4,5,...

    Text Solution

    |

  8. The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is [0,pi/2] (b) (0,pi/6) ...

    Text Solution

    |

  9. The range of the function f(x)=(e^x-e^(|x|))/(e^x+e^(|x|)) is (a)(-oo,...

    Text Solution

    |

  10. Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] deno...

    Text Solution

    |

  11. The range of the function f defined by f(x)=[1/(sin{x})] (where [.] an...

    Text Solution

    |

  12. Range ofthe function f(x)=cos(Ksin x) is [-1,1], then the least positi...

    Text Solution

    |

  13. Let f(x)=sqrt(|x|-|x+)(w h e r e{dot} denotes the fractional part of (...

    Text Solution

    |

  14. The range of f(x)=cos^(-1)((1+x^2)/(2x))+sqrt(2-x^2) is (a){0,1+pi/2} ...

    Text Solution

    |

  15. The range of the following function is f(x)=sqrt((1-cosx)sqrt((1-cosx)...

    Text Solution

    |

  16. The range of f(x)=(x+1)(x+2)(x+3)(x+4)+5 for x in [-6,6] is [4, 5045] ...

    Text Solution

    |

  17. The range of f(x)=sec^(-1)((log)3tanx+(log)(tanx)3) is (a)[pi/3,pi/2)...

    Text Solution

    |

  18. The domain of definition of the function f(x)={x}^({x})+[x]^([x]) is w...

    Text Solution

    |

  19. 49. If [x^2-2x + a] = 0 has no solution then

    Text Solution

    |

  20. If [x] and {x} represetnt the integral and fractional parts of x , res...

    Text Solution

    |