Home
Class 12
MATHS
If f(x)=sin{[x+5]+{x-{x-{x}}}" for "x in...

If `f(x)=sin{[x+5]+{x-{x-{x}}}" for "x in (0,pi/4)` is invertible, where {.} and [.] represent fractional part and greatest integer functions respectively, then `f^(-1) (x)` is ::
`I. sin^(-1)x` II. `pi/2-cos^(-1)x` III. `sin^(-1){x}` IV`.cos^(-1){x}`
The correct choice is:

A

`sin^(-1)x`

B

`(pi)/(2) - cos^(-1)x`

C

`sin^(-1) {x}`

D

`cos^(-1){x}`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • SETS , RELATIONS AND FUNCTIONS

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS (SINGLE OPTION CORRECT TYPE)|44 Videos

  • QUADRATIC EQUATIONS

    MTG-WBJEE|Exercise WB JEE Previous Years Questions (One or More than One Option Correct Type) |7 Videos

  • SOLUTION OF TRIANGLES

    MTG-WBJEE|Exercise WB JEE (Previous Years Questions) CATEGORY 2: Single Option Correct Type|1 Videos

Similar Questions

Explore conceptually related problems

Find the range of each of the following functions: (where {.} and [.] represents fractional part and greatest integer part functions respectively) f(x)=[1/(sin{x})]

For the function f(x) = sin (pi[x]) xx cos^(-1)([x]) , choose the correct option. (where [.] represents the greatest integer function)

" The range of the function "f(x)=sin(sin^(-1)[x^(2)-1])" is (where "[" .] represents greatest integer function) "

The range of the function f(x)=sin(sin^(-1)[x^(2)-1]) is (where[*] represents greatest integer function)

Period of f(x)=e^(cos x)+sin pi[x] is (l.] and {.} denotes the greatest integer function and fractional part function respectively)

Let [x] be the greatest integer function f(x)=((sin((1)/(4)(pi[x])))/([x])) is

Let f(x) = ([x] - ["sin" x])/(1 - "sin" [cos x]) and g (x) = (1)/(f(x)) and [] represents the greatest integer function, then

The domain of f(x)=e^(sin(x-[x]))-[x]cos(pi/([x-1])) ,where [*] represents greatest integer function,is

The function f(x)=cos^(-1)((2[sin x|+|cos x|])/(sin^(2)x+2sin x+(11)/(4))) is defined if x belongs to (where [.] represents the greatest integer function)

f(x)=1+[cos x]x in 0<=x<=(pi)/(2) (where [.] denotes greatest integer function)

MTG-WBJEE-SETS , RELATIONS AND FUNCTIONS-WB JEE PREVIOUS YEARS QUESTIONS (SINGLE OPTION CORRECT TYPE)
  1. If f(x)=sin{[x+5]+{x-{x-{x}}}" for "x in (0,pi/4) is invertible, where...

    Text Solution

    |

  2. Let f : R rarr R be such that f is injective and f(x) f(y ) = f(x+ y...

    Text Solution

    |

  3. We define a binary relationon ~ on the set of all 3 xx 3 real matrices...

    Text Solution

    |

  4. The number of onto functions from the set {1,2,...., 11} to the set {1...

    Text Solution

    |

  5. LEt f(x)=2^(100)x+1 and g(x)=3^(100)x+1 Then the set of real numbers x...

    Text Solution

    |

  6. For any two real numbers a and b, we define a R b if and only if sin^2...

    Text Solution

    |

  7. The minimum value of the function f(x) = 2|x - 1| + |x - 2| is

    Text Solution

    |

  8. Let the number of elements of the sets A and B be p and q respectively...

    Text Solution

    |

  9. Let R be the set of all real numbers and f : Rrarr R be given by f(x) ...

    Text Solution

    |

  10. The function f(x)=x^(2)+bx+c, where b and c are real constants, descri...

    Text Solution

    |

  11. Find the range of the function f(x)=3 sin (sqrt((pi^(2))/(16)-x^(2))).

    Text Solution

    |

  12. There is a group of 265 persons who like either singing or dancing or ...

    Text Solution

    |

  13. The number of real roots of equation log(e )x + ex = 0 is

    Text Solution

    |

  14. If f:[0,pi/2)->R is defined as f(theta)=|(1,tantheta,1),(-tantheta,1,...

    Text Solution

    |

  15. Let f:R-> R be defined as f(x)=(x^2-x+4)/(x^2+x+4). Then the range of ...

    Text Solution

    |

  16. Let S={a,b,c}epsilonNxxNxxN:a+b+c=21,a<=b<=c} and T={(a,b,c)epsilon Nx...

    Text Solution

    |

  17. Let R be a relation defined on the set Z of all integers and x Ry whe...

    Text Solution

    |

  18. if A={5^(n)-4n-1: n in N} and B={16(n-1):n in N} then

    Text Solution

    |

  19. If the function R to R is defined by f(x)=(x^2+1)^(35)AA in R then f ...

    Text Solution

    |

  20. Let P be the set of all non-singular matrices of order 3 over ú and Q ...

    Text Solution

    |

  21. On the set R of real numbers we defined xPy i and only if xylt 0. T...

    Text Solution

    |