Home
Class 12
MATHS
The range of the function f(x)=(x^2+x+2)...

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)` `(1,7/3)` (d) `(1,7/5)`

A

`(1, oo)`

B

`(1, 11//7]`

C

`[1, 7//3]`

D

`(1, 7//5]`

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, f(x) is defined for all `x in R`
So, domain (f) = R. Let f(x) = y Then,
`(x^(2) +x +2)/(x^(2) + x +1) = y`
`rArr x^(2) (y-1) + (y-2) ge 0`
Also, `y ne 1` for any `x in R`. Hence range of `f(x) = [1,7//3]`
Promotional Banner

Topper's Solved these Questions

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|94 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|63 Videos

Similar Questions

Explore conceptually related problems

The range of the function f(x)=x^2+1/(x^2+1) is

The range of the function f(x)=x^2+1/(x^2+1) is

The range of the function f(x) = 3x^2+7x+10 is

The range of the function f(x)=tan^(- 1)((x^2+1)/(x^2+sqrt(3))) x in R is

The range of the function f(x)=(x^2-x)/(x^2+2x) is R (b) R-[1] (c) R={-1/2,1} (d) none of these

The range of the function f(x)=(x+2)/(|x+2|),\ x!=-2 is {-1,1} b. {-1,0,1} c. {1} d. (0,oo)

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

Find the domain and range of the function f={(x :1/(1-x^2)): x in R , x!=+-1}dot

The interval of increase of the function f(x)=x-e^x+tan(2pi//7) is (a) (0,\ oo) (b) (-oo,\ 0) (c) (1,\ oo) (d) (-oo,\ 1)

The range of the function f(x)=x/(|x|) is a. R-{0} b. R-{-1,1} c. {-1,1} d. none of these

OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Section I - Solved Mcqs
  1. Let f:(4,6)vec(6,8) be a function defined by f(x)=x+[x/2]dotw h e r e[...

    Text Solution

    |

  2. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  3. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo)...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. If f: RvecS , defined by f(x)=sinx-sqrt(3)cosx+1,is onto , then find ...

    Text Solution

    |

  6. The graph of the function y=f(x) is symmetrical about the line x=2, th...

    Text Solution

    |

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

    Text Solution

    |

  8. find the value of the

    Text Solution

    |

  9. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |

  10. Let f(x)=sin((pi)/(6)sin((pi)/(2)sinx)) " for all "x in R and g(x)=(pi...

    Text Solution

    |

  11. Consider the function f defined on the set of all non-negative interg...

    Text Solution

    |

  12. In a function 2f(x)+ xf(1/x)-2f(|sqrt2sin(pi(x+1/4))|)=4cos^2[(pix)/2]...

    Text Solution

    |

  13. Let X be the set of all positive such that f(x+y) = f(xy) for all x g...

    Text Solution

    |

  14. f(x) = 9^x/ ( 9 + 9^x) then value of f(1/2015) + f(2/2015) .......+ f(...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. Consider the function g(x) defined as g(x),(x^((2^(2011)-1))-1)=(x+1)(...

    Text Solution

    |

  17. Let f(n)=1+1/2+1/3++1/ndot Then f(1)+f(2)+f(3)++f(n) is equal to nf(n)...

    Text Solution

    |

  18. The period of the function f(x)=4sin^(4) ((4x-3pi)/(6pi^(2)))+2 cos ((...

    Text Solution

    |

  19. If f(x) = log([x-1])(|x|)/(x),where [.] denotes the greatest integer ...

    Text Solution

    |

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

    Text Solution

    |