Home
Class 12
MATHS
Let f(x+y)=f(x)+f(y) for all xa n dydot ...

Let `f(x+y)=f(x)+f(y)` for all `xa n dydot` If the function `f(x)` is continuous at `x=0,` show that `f(x)` is continuous for all `xdot`

Promotional Banner

Topper's Solved these Questions

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Coordinates and Straight Lines

    A DAS GUPTA|Exercise EXERCISE|111 Videos

Similar Questions

Explore conceptually related problems

Let f(x+y)=f(x)+f(y) for all x and y If the function f(x) is continuous at x=0 show that f(x) is continuous for all x

Let f(x+y) = f(x) + f(y) for all x and y. If the function f (x) is continuous at x = 0 , then show that f (x) is continuous at all x.

Leg f(x+y)=f(x)+f(y) for all x,y in R, If f(x) is continuous at x=0, show that f(x) is continuous at all x.

If f((x + 2y)/3)=(f(x) + 2f(y))/3 AA x, y in R and f(x) is continuous at x = 0. Prove that f(x) is continuous for all x in R.

Let f(x+y)=f(x)+f(y)AA x, y in R If f(x) is continous at x = 0, then f(x) is continuous at

if f(x+y)=f(x)+f(y)+c, for all real x and y and f(x) is continuous at x=0 and f'(0)=-1 then f(x) equals to

Let f (x+y)=f (x) f(y) AA x, y in R , f (0)ne 0 If f (x) is continous at x =0, then f (x) is continuous at :

A function f(x) satisfies the following property: f(x.y)=f(x)f(y). Show that the function f(x) is continuous for all values of x if it is continuous at x=1

A DAS GUPTA-Continuity, Differentiability and Graph of Function-Exercise
  1. Consider the function f defines by f(x) = x-[x], where[x] denotes the ...

    Text Solution

    |

  2. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

    Text Solution

    |

  3. Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is contin...

    Text Solution

    |

  4. Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x)i scon t inuou sa tx=...

    Text Solution

    |

  5. Let f (x+y)=f (x) f(y) AA x, y in R , f (0)ne 0 If f (x) is continous ...

    Text Solution

    |

  6. Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x)...

    Text Solution

    |

  7. The set of all points, where the function f (x) = x/(1+|x|) is dif...

    Text Solution

    |

  8. The set of points where ,f(x) = x|x| is twice differentiable is

    Text Solution

    |

  9. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

    Text Solution

    |

  10. Let f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3...

    Text Solution

    |

  11. Draw the graph of the function and discuss the continuity and differen...

    Text Solution

    |

  12. Given the function f(x) = 1/( 1-x) , The points of discontinuity of th...

    Text Solution

    |

  13. If f(x)={:{(ax^(2)-b", for " 0 le x lt1),(2", for " x=1),(x+1", for " ...

    Text Solution

    |

  14. If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2...

    Text Solution

    |

  15. Let f(x)=( x^2+3x-10)/(x-2), x=!2. The value f(2) = will make the fun...

    Text Solution

    |

  16. If f(x) is continuous in [0,1] and f(1/2)=1. prove that lim(n->oo)f((...

    Text Solution

    |

  17. If f(x) =(sin (e^(x-2)-))/(log(x-1)) then lim(xto2)f(x) is given by

    Text Solution

    |

  18. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

    Text Solution

    |

  19. The function f(x) = (log(1+ax)-log(1-bx))/x is not difined at x = 0. ...

    Text Solution

    |

  20. The function f(x)={{:(|x-3|",", x ge1),(((x^(2))/(4))-((3x)/(2))+(13)/...

    Text Solution

    |