Home
Class 12
MATHS
The domain of f(x)=((log)2(x+3))/(x^2+3x...

The domain of `f(x)=((log)_2(x+3))/(x^2+3x+2)` is (a)`R-{-1,2}` (b) `(-2,oo)` (c)`R-{-1,-2,-3}` (d) `(-3,oo)-(-1,-2}`

A

`R-{-1,-2}`

B

`(-2,oo)`

C

`R-{-1,-2,-3}`

D

`(-3,oo)-{-1,-2}`

Text Solution

Verified by Experts

The correct Answer is:
D
Here, `x+3 gt 0 " and " x^(2)+3x+2 ne 0.`
Therefore, `x gt -3 " and " (x+1)(x+2) ne 0, "i.e.," x ne -1,-2.`
Therefore, the domain is `(-3,oo)-{-1,-2}.`
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

The domain of the function f(x)=(log)_(3+x)(x^2-1) is

The domain of definition of f(x) = (log_2(x+2))/(x^2+3x+2)

the domain of the function f(x) = ( log (x+3))/(x^2 +3x +2) is

The domain of the function f(x)=sqrt(log_((|x|-1))(x^2+4x+4)) is (a) (-3,-1)uu(1,2) (b) (-2,-1)uu(2,oo) (c) (-oo,-3)uu(-2,-1)uu(2,oo) (d)none of these

The domain of the function f(x)=sqrt(log(1/(|sinx|))) (a) R-{-pi,pi} (b) R-{npi|npiZ} (c) R-{2npi|n in z} (d) (-oo,oo)

The domain of f(x)=cos^(-1)((2-|x|)/4)+[ log(3-x)]^-1 is (a) [-2,6] (b) [-6,2)uu(2,3) [-6,2] (d) [-2,2]uu(2,3)

The domain of the function f(x)=(sin^(-1)(3-x))/(I n(|x|-2))i s [2,4] (b) (2,3)uu(3,4] (c) (0,1)uu(1,oo) (d) (-oo,-3)uu(2,oo)

The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d) oo

The domain of the function f(x)=sin^(-1)((8(3)^(x-2))/(1-3^(2(x-1)))) is

The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo) (b) (1,(11)/7) (c) (1,7/3) (d) (1,7/5)

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. The domain of the function f(x)=(1)/(sqrt(""^(10)C(x-1)-3xx""^(10)C(x)...

    Text Solution

    |

  2. The domain of the function f(x)=(sin^(-1)(3-x))/("In"(|x|-2)) is

    Text Solution

    |

  3. The domain of f(x)=((log)2(x+3))/(x^2+3x+2) is (a)R-{-1,2} (b) (-2,oo...

    Text Solution

    |

  4. The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the gre...

    Text Solution

    |

  5. The domain of the function f(x)=(log)(3+x)(x^2-1) is (-3,-1)uu(1,oo) ...

    Text Solution

    |

  6. Domain of the function, f(x)=[log10 ((5x-x^2)/4)]^(1/2) is

    Text Solution

    |

  7. The domain of f(x)="log"|logx|i s (a)(0,oo) (b) (1,oo) (c) (0,1)uu(1...

    Text Solution

    |

  8. If x^3f(x)=sqrt(1+cos2x)+|f(x)|, (-3pi)/4ltxlt(-pi) /2 and f(x)=(alpha...

    Text Solution

    |

  9. The function f(x)=(sec^(-1)x)/(sqrt(x)-[x]), where [x] denotes the gre...

    Text Solution

    |

  10. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |

  11. The domain of f(x)=cos^(-1)((2-|x|)/4)+[l log(3-x)]^1 is [-2,6] (b...

    Text Solution

    |

  12. The domain of the function f(x)=sqrt(log(1/(|sinx|))) R-{-pi,pi} (b)...

    Text Solution

    |

  13. Domain of definition of the function f(x) = log2 (-log(1/2) (1+x^(-4))...

    Text Solution

    |

  14. The number of real solutions of the (log)(0. 5)|x|=2|x| is (a) 1 (b) ...

    Text Solution

    |

  15. Let f: Rvec[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the s...

    Text Solution

    |

  16. The domain of the function f(x)=sqrt("In"((|x|-1))(x^(2)+4x+4)) is

    Text Solution

    |

  17. The domain of f(x)=1n(a x^3+(a+b)x^2+(b+c)x+c), where a >0,b^2-4a c=0,...

    Text Solution

    |

  18. The domain of the function f(x)=1/(sqrt(4x=|x^2-10 x+9})) is (7-sqrt(...

    Text Solution

    |

  19. The domain of the function f(x)=(1)/(sqrt(|cosx|+cosx)) is

    Text Solution

    |

  20. The exhaustive domain of the following function is f(x)=sqrt(x^(12)-x^...

    Text Solution

    |