Home
Class 12
MATHS
The range of the function f(x) = sin^(-1...

The range of the function `f(x) = sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2]`, where [ . ] denotes the greatest integer function.

A

`{(pi)/2,pi}`

B

`{0,(pi)/2}`

C

`{pi}`

D

`(0,(pi)/2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-II|20 Videos
  • FUNCTION

    FIITJEE|Exercise COMPREHENSIONS|8 Videos
  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-II|17 Videos
  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos
  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

Similar Questions

Explore conceptually related problems

f(x)=sin^(-1)[x^(2)+(1)/(2)]+cos^(-1)[x^(2)-(1)/(2)] where [.1 denotes the greatest integer function.

The range of the function y=2sin^(-1)[x^(2)+(1)/(2)]+cos^(-1)[x^(2)-(1)/(2)] is (where, [.] denotes the greatest integer function)

The number of elements in the range of functions: y=sin^(-1) [x^(2)+5/9]+cos^(-1) [x^(2)-4/9] where where [.] denotes the greatest integer function is:

f(x)= cosec^(-1)[1+sin^(2)x] , where [*] denotes the greatest integer function.

The range of sin^(-1)[x^(2)+(1)/(2)]+cos^(-1)[x^(2)-(1)/(2)], where [.] denotes the greatest integer function,is {(pi)/(2),pi}(b){pi}(c){(pi)/(2)}(d) none of these

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then

f(x)=1/sqrt([x]^(2)-[x]-6) , where [*] denotes the greatest integer function.

The range of the function f(x)=(sin(pi[x^(2)+1]))/(x^(4)+1), where [.] denotes the greatest integer function,is

f(x)=sin^(-1)[log_(2)((x^(2))/(2))] where [.] denotes the greatest integer function.

The range of the function f(x)=sin^(-1)[x^(2)-(1)/(3)]-cos^(-1)[x^(2)+(2)/()] is (where, [x] represents the greatest integer value of x)

FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (OBJECTIVE) Level-I
  1. If k sin^(2)x+(1)/(k) cosec^(2) x=2, x in (0,(pi)/(2)), then cos^(2...

    Text Solution

    |

  2. The exhausiive Intervals of real values of x such that sqrt(12-4x)gt1+...

    Text Solution

    |

  3. The range of the function f(x) = sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2], ...

    Text Solution

    |

  4. If fog = abs(sin x) and gof = sin^(2)x then f(x) and g(x) are:

    Text Solution

    |

  5. Let S={(x,y):abs(abs(absx-2)-1)+abs(abs(absy-2)-1)=1). If S is made ou...

    Text Solution

    |

  6. The domain of f(x) = sqrt(log(1//4)((5x-x^(2))/4))+""^(10)C(x) is

    Text Solution

    |

  7. If f is a function such that f(0)=2,f(1)=3,a n df(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  8. function f(x) =sin^(-1)(x-x^2)+sqrt(1-1/|x|+1/[x^2-1]) is defined in t...

    Text Solution

    |

  9. The range of f(x) =sin(sin^(-1){x}). where { ·} denotes the fractional...

    Text Solution

    |

  10. Range of f(x)=cos^(- 1)x+2sin^(- 1)x+3tan^(- 1)x is

    Text Solution

    |

  11. If f(x)=sin(sqrt([a])x) (where [.] denotes the greatest integer functi...

    Text Solution

    |

  12. If f(x)={x, when x is rational, 1-x, when x is irrational , then

    Text Solution

    |

  13. If f:Rto(1,10), where f(x)=(x^(2)+1-alpha)/(x^(2)+2) is an onto functi...

    Text Solution

    |

  14. If f(x)=cos |x| + [|(sinx)/2|], (where [.] denotes the greatest intege...

    Text Solution

    |

  15. The range of function f(x) = sqrt(.^(x^2+4x)C(2x^2+3)) is

    Text Solution

    |

  16. The curve y = f(x) is symmetric about the lines (10^(4)- 1)x + 2(10^(4...

    Text Solution

    |

  17. If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distin...

    Text Solution

    |

  18. lf domain of f(x) is [-1, 2] then domain of f([x]-x^2+4) where [.] den...

    Text Solution

    |

  19. Period of the function f(x) = [5x + 7] + cospix - 5x where [·] denotes...

    Text Solution

    |

  20. The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in ...

    Text Solution

    |