Home
Class 11
MATHS
Let g(x)=1+x-[x] and f(x)={{:(-1",", x l...

Let `g(x)=1+x-[x]` and `f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0):}`, then for all `x`, `f[g(x)]` is equal to

A

x

B

1

C

f (x)

D

g (x)

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|83 Videos

  • PROBABILITY

    TARGET PUBLICATION|Exercise EVALUATION TEST|8 Videos

  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=1+x-[x] "and " f(x)={{:(-1","x lt 0),(0","x=0),(1","x gt 0):} Then, for all x, find f(g(x)).

If f(x) = {(x-1,",", x lt 0),(1/4,",",x = 0),(x^2,",",x gt 0):}

Let g(x)=1=x-[x] and f(x)={-1, x < 0 , 0, x=0 and 1, x > 0, then for all x, f(g(x)) is equal to (i) x (ii) 1 (iii) f(x) (iv) g(x)

Let g(x) = 1 + x – [x] and f(x)={:{(-1,if,xlt0),(0,if, x=0),(1,if,x gt0):} then Aax, fog(x) equals (where [ * ] represents greatest integer function).

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 g(x)=1+x-[x] and f(x)=-1 if x 0, then f|g(x)]=1x>0

If f(x)={{:(,|x|+1, x lt 0),(, 0,x=0),(,|x|-1, x gt 0):}" then "underset(x to a)lim f(x) exists for all

If f(x) ={(|x|,",",x lt 0),(x,",",0 le x le 1),(1,",",x gt 1):} , then f(x) is discontinuous at

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

TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. If f(x) =2x +1 and g (x) (x-1)/(2) for all real x, then (fog) ^(-1)( (...

    Text Solution

    |

  2. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1, then (gof)(x...

    Text Solution

    |

  3. Let g(x)=1+x-[x] and f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0)...

    Text Solution

    |

  4. Two functions f:Rrarr R, g:R rarr R are defined as follows : f(x)={{...

    Text Solution

    |

  5. If f:R->R and g:R->R is given by f(x) =|x| and g(x)=[x] for each x in ...

    Text Solution

    |

  6. Let the function f, g, h are defined from the set of real numbers RR t...

    Text Solution

    |

  7. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1, then (gof)(x...

    Text Solution

    |

  8. Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x sat...

    Text Solution

    |

  9. Let f,g: RvecR be a two function defined as f(x)=|x|+xa n dg(x)=|x|-x ...

    Text Solution

    |

  10. The period of f (x) =x - [x], if it is periodic is

    Text Solution

    |

  11. If f: R rarr R be defined by f(x) =e^(x) and g:R rarr R be defined b...

    Text Solution

    |

  12. If f: R to R be defined by f(x) =(1)/(x), AA x in R. Then , f is

    Text Solution

    |

  13. If f : A to B is bijection and g : B to A is that inverse of f, then ...

    Text Solution

    |

  14. If A={1,2,3,4}" and "B={1,2,3,4,5,6} are two sets and function f: A to...

    Text Solution

    |

  15. A is a set having 6 distinct elements. The number of distinct function...

    Text Solution

    |

  16. Number of bijective function from a set of 10 elements to itself is

    Text Solution

    |

  17. Set A has 3 elements and set B has 4 elements. The number of injection...

    Text Solution

    |

  18. The set A has 4 elements and thse set B has 5 elements, then the numbe...

    Text Solution

    |

  19. Which one of the following is a bijective function on the set of real ...

    Text Solution

    |

  20. Let f : R to R be defined by f (x) = x ^(4), then

    Text Solution

    |