Home
Class 12
MATHS
Let [x] = greatest integer le x and {x} ...

Let [x] = greatest integer `le x` and `{x} =x - [x]`,
Let, `f_(1)(x) = 2/pi [sin^(-1) (x) + cos^(-1)(x)]`
`f_(2)(x) = sin^(2) (log_(5)x) + cos^(2) (log_(3)x)`
`f_(3)(x) = sgn({x} +1)`
and `f_(4)(x) = sec^(2) [{x}] - tan^(2) {[x]}`
`sgn(x) = {{:(-1, if x lt 0),(0, if x=0),(1, if gt 0):}`
Then which of the follwing is not true?

A

`f_(1) =f_(2)`

B

`f_(1) = f_(3)`

C

`f_(1) = f_(4)`

D

`f_(3) = f_(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS )|20 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MCGROW HILL PUBLICATION|Exercise EXERCISE (CONCEPT -BASED (SINGLE CORRECT ANSWER TYPE QUESTIONS) )|45 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 1 (SINGLE CORRECT ANSWER TYPE QUESTIONS) )|30 Videos

  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from previous Years. B - architecture entrance examination papers|16 Videos

  • STATISTICS

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|13 Videos

Similar Questions

Explore conceptually related problems

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

Suppose [x] = greatest integer le x Let f(x) = sin^(-1)[x^(2) + 1/2]-cos^(-1)[x^(2)-1/2] , Then range of f is:

Let [x]= greatest integer le x and f(x) = cos([pi^(2)]x) + sin([e^(2)]x) then f(pi//4) is equal to

f(x)=(sin^(-1)x)^(2)*cos((1)/(x))ifx!=0;f(0)=0,f(x)

Let g(x) = x - [x] - 1 and f(x) = {{:(-1", " x lt 0),(0", "x =0),(1", " x gt 0):} [.] represents the greatest integer function then for all x, f(g(x)) = .

Let f(x)={{:(x^2+4x "," -3 le x le 0),(-sin x ","0 lt x le pi//2 ),(-cos x -1 "," pi//2 lt x le pi):} which one of the following is not true ?

Let F (x) = [{:(cos x , -sin x , 0),(sin x , cos x , 0),(0 , 0, 1):}] , then

If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative of f(x) x=0

Let f(x)={{:(x^(2) sin ((pix)/(2)),-1 lt x lt 1, x ne 0),(x|x|, x gt 1 or x le -1):} . Then ,

MCGROW HILL PUBLICATION-SETS, RELATIONS AND FUNCTIONS-SOLVED EXAMPLES (LEVEL 2 (SINGLE CORRECT ANSWER TYPE QUESTIONS))
  1. If g(x)=x^(2)+x+x-1 and g(f(x))=4x^(2)-10x+5 then find f((5)/(4))

    Text Solution

    |

  2. Suppose a, b, c, d be four distinct real numbers. Let A = {a, b} and B...

    Text Solution

    |

  3. Suppose A(1),A(2),…………A(45) are 45 sets each having 6 elements and B(1...

    Text Solution

    |

  4. Let A and B be two sets defined as follows: A = {n in N : 2^(2^(n))...

    Text Solution

    |

  5. Let f(x) = sin(2x) + x-|x| AA x in R (where [x] = greatest integer le ...

    Text Solution

    |

  6. Let f(x) = 3x + 5 AA x in R, g^(-1)(x) = x^(3) +1 AA x in R, then (f^(...

    Text Solution

    |

  7. Suppose f,g, R to R. If g(x) defined by g(x) = x^(2) + x-2 and (g.f)(x...

    Text Solution

    |

  8. The domain of the function f(x) = sqrt((4-x^(2))/([x]+2)) where [x] d...

    Text Solution

    |

  9. The domain of f(x) = sqrt(cos^(-1)((1-|x|)/3)) is

    Text Solution

    |

  10. The domain of f(x) = 1/sqrt(x^(16) -x^(13) + x^(4) -x +1), is

    Text Solution

    |

  11. The domain of f(x) = sqrt(1-sqrt(1-sqrt(1-sqrt(1-x^(2))))), is

    Text Solution

    |

  12. The domain of f(x) = log(3)log(4)log(5)(x) is

    Text Solution

    |

  13. If [x] denotes the greatest integer le x, then domain of f(x) = 1/sq...

    Text Solution

    |

  14. The domain of f(x=1/(sqrt(|cosx|+cosx)) is [-2npi,2npi],n in Z 2np...

    Text Solution

    |

  15. The value of n in N for which the function f(x) = (sin(nx))/(sin (x/...

    Text Solution

    |

  16. Let [x] = greatest integer le x and {x} =x - [x], Let, f(1)(x) = 2/p...

    Text Solution

    |

  17. Let A, B and C be three non-empty sets. Suppose f : A to B and g : B ...

    Text Solution

    |

  18. Let f: R of R be a function defined by f(x) =x^(3) + px^(2) + 7x + ...

    Text Solution

    |

  19. Let A =[-1,1]. Define a relation R on A as follows: a, b in A, aRb i...

    Text Solution

    |

  20. Let A be a set containing n elements. If the number of reflexive relat...

    Text Solution

    |