Home
Class 11
MATHS
If f:R->R and g:R->R is given by f(x) =|...

If `f:R->R` and `g:R->R` is given by f(x) =|x| and g(x)=[x] for each `x in R` then `{x in R:g(f(x))le f(g(x))}`

A

`Zuu (-oo, 0)`

B

`(-oo, 0)`

C

`Z`

D

R

Text Solution

Verified by Experts

The correct Answer is:
D
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

If f:R rarr R and g:R rarr R is given by f(x)=|x| and g(x)=[x] for each x in R then {x in R:g(f(x))<=f(g(x))}

If f:R rarr R and g:R rarr R are defined by f(x)=x-[x] and g(x)=[x] is x in R then f{g(x)}

Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for all x to R . Then,

If f:R rarr R and g:R rarr R given by f(x)=x-5 and g(x)=x^(2)-1, Find fog

If f: R->R and g: R->R be functions defined by f(x)=x^2+1 and g(x)=sinx , then find fog and gof .

If f : R -> R and g : R -> R defined f(x)=|x| and g(x)=[x-3] for x in R [.] denotes the greatest integer function then {g(f(x)):(-8)/(5)ltxlt(8)/(5)} =

Let f: R->R and g: R->R be defined by f(x)=x^2 and g(x)=x+1 . Show that fog!=gofdot

Find gof and fog when f: R->R and g: R->R is defined by f(x)=x and g(x)=|x|

If f:R rarr R and g:R rarr R defined f(x)=|x| and g(x)=[x-3] for x in R[.] denotes the greatest integer function

Let f : R to R and g : R to R be given by f (x) = x^(2) and g(x) =x ^(3) +1, then (fog) (x)

TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. Let g(x)=1+x-[x] and f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Let the function f:R to R be defined by f(x)=2x+sin x. Then, f is

    Text Solution

    |

  20. Let f:N-&gt;N be defined by f(x)=x^2+x+1,x in N. Then is f is

    Text Solution

    |