Home
Class 11
MATHS
Let g(x)=1+x-[x] and f(x)={-1,x < 0 0,...

Let `g(x)=1+x-[x] and f(x)={-1,x < 0 0, x=0 1, x > 0.` Then for all `x,f(g(x))` is equal to (where [.] represents the greatest integer function). (a) `x` (b) `1` (c) `f(x)` (d) `g(x)`

A

x

B

1

C

f(x)

D

g(x)

Text Solution

Verified by Experts

The correct Answer is:
B
We know that
`0 le x-[x] lt 1"for all " x in R`
`Rightarrow 1 le 1 +x-[x] lt 2"for all "x in R`
`Rightarrow 1 le g(x)lt 2" for all "x in R`
`Rightarrow f(g(x))=2" for all "x in R`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|48 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=1+x-[x]a n df(x)={-1, x 0 . Then for all x ,f(g(x)) is equal to (where [.] represents the greatest integer function). (a) x (b) 1 (c) f(x) (d) g(x)

if f(x) ={{:((1-|x|)/(1+x),xne-1),(1, x=-1):} then f([2x]) , where [.] represents the greatest integer function , is

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| and g(x)=[x] , (where [.] denotes the greatest integer function) Then, (fog)'(-1) is

If f(x)= sin^(-1)x and g(x)=[sin(cosx)]+[cos(sinx)], then range of f(g(x)) is (where [*] denotes greatest integer function)

If f(x)=|x-1|" and "g(x)=f(f(f(x))) , then for xgt2,g'(x) is equal to

Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the greatest integer function . Then h(-1) is

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

Let f(x)=cos x and g(x)=[x+1],"where [.] denotes the greatest integer function, Then (gof)' (pi//2) is

Let f:(2,4)->(1,3) where f(x) = x-[x/2] (where [.] denotes the greatest integer function).Then f^-1 (x) is

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Section I - Solved Mcqs
  1. Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=...

    Text Solution

    |

  2. If f:[1,oo) to [2, oo)" is given by " f(x)=x+(1)/(x), " then " f^(-1)(...

    Text Solution

    |

  3. Let g(x)=1+x-[x] and f(x)={-1,x < 0 0, x=0 1, x > 0. Then for all...

    Text Solution

    |

  4. Let f(x)=(alphax)/((x+1)),x!=-1. for what value of alpha is f(f(x))=x ...

    Text Solution

    |

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

    Text Solution

    |

  6. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  7. Let f :R->R be a function defined by f(x)=|x] for all x in R and let A...

    Text Solution

    |

  8. The function f:(-oo,-1)vec(0, e^5) defined by f(x)=e^x^(3-3x+2) is man...

    Text Solution

    |

  9. If the functions f, g and h are defined from the set of real numbers R...

    Text Solution

    |

  10. The distinct linear functions which map [-1, 1] onto [0, 2] are f(x...

    Text Solution

    |

  11. The values of a and b for which the map f: R to R, given by f(x)=ax+b(...

    Text Solution

    |

  12. Find the value of parameter alpha for which the function f(x)=1+alp...

    Text Solution

    |

  13. Let f:(2,oo)to X be defined by f(x)=4x-x^(2). Then f is invertible, if...

    Text Solution

    |

  14. If f:R->S defined by f(x)=sinx-sqrt(3)cosx+1 is onto , then the interv...

    Text Solution

    |

  15. If f(x)={{:(,|x|, x le1),(,2-x,x gt 1):}, then fof (x) is equal to

    Text Solution

    |

  16. Let A={x-1 le x le 1} and f:A to A such that f(x)=x|x| then f is:

    Text Solution

    |

  17. If f: R->(-1,\ 1) is defined by f(x)=(-x|x|)/(1+x^2) , then f^(-1)(x) ...

    Text Solution

    |

  18. Let f: R->R be given by f(x)=[x]^2+[x+1]-3 , where [x] denotes the gre...

    Text Solution

    |

  19. Let M be the set of all 2xx2 matrices with entries from the set R o...

    Text Solution

    |

  20. The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and on...

    Text Solution

    |