Home
Class 12
MATHS
f (x)=[x] and g (x)= {{:( 0"," , x in I ...

`f (x)=[x] and g (x)= {{:( 0"," , x in I ),( x ^(2)"," , cancel(in)I):}` where [.] dentoes the greatest integer function. Then

A

gof is continous for all x

B

gof is not continous for all x

C

fog is continous everywhere

D

fog is not continous everywhere

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|29 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|3 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|22 Videos
  • COMPOUND ANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VK JAISWAL ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

Let f(x) = [x]^(2) + [x+1] - 3 , where [.] denotes the greatest integer function. Then

f(x)=[x] and g(x)={{:(1",",x gt1),(2",", x le 1):} , (where [.] represents the greatest integer function). Then g(f(x)) is discontinuous at x = _______________

If f(x)=([x])/(|x|), x ne 0 , where [.] denotes the greatest integer function, then f'(1) is

If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) is

Given lim_(x to 0)(f(x))/(x^(2))=2 , where [.] denotes the greatest integer function, then

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) ={{:(2x-[x]+ xsin (x-[x]),,x ne 0) ,( 0,, x=0):} where [.] denotes the greatest integer function then

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

VK JAISWAL ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. If f (x) be a differentiable function satisfying f (y) f ((x)/(y))=f (...

    Text Solution

    |

  2. Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...

    Text Solution

    |

  3. let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...

    Text Solution

    |

  4. Let y=e^x s in x^3+(t a n x)^xdotF in d(dy)/(dx)dot

    Text Solution

    |

  5. Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x...

    Text Solution

    |

  6. Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...

    Text Solution

    |

  7. If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),...

    Text Solution

    |

  8. If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) ...

    Text Solution

    |

  9. Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ...

    Text Solution

    |

  10. If f(x)={|x|-3 x < 1|x-2|+a x >= 1 & g(x)={2-|x| x < 2 sgn(x)-b x >= 2...

    Text Solution

    |

  11. Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln...

    Text Solution

    |

  12. f (x) is differentiable function satisfying the relationship f ^(2) (x...

    Text Solution

    |

  13. The function f (x)=[sqrt(1-sqrt(1-x ^(2)))],(where [.] denotes greates...

    Text Solution

    |

  14. A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...

    Text Solution

    |

  15. The points of discontinuities of f (x)= [(6x)/(pi)]cos [(3x)/(pi)]"in"...

    Text Solution

    |

  16. Check the continuity of f(x) = {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+...

    Text Solution

    |

  17. If x=phi (t), y=psi(t), then (d ^(2)y)/(dx ^(2))=

    Text Solution

    |

  18. f (x)=[x] and g (x)= {{:( 0"," , x in I ),( x ^(2)"," , cancel(in)I)...

    Text Solution

    |

  19. Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) th...

    Text Solution

    |

  20. Let f (x)=[{:((3x-x ^(2))/(2),,, x lt 2),([x-1],,, 2 le x lt 3),( x ^(...

    Text Solution

    |