Home
Class 12
MATHS
If f : R to R is continuous such that ...

If ` f : R to R ` is continuous such that
` f(x + y) = f(x) + f(y) x in R , y in R ` and
f(1) = 2 then f(100) =

A

100

B

50

C

200

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND CONTINUITY

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise 2(Special Type Questions)|10 Videos

  • LIMITS AND CONTINUITY

    DIPTI PUBLICATION ( AP EAMET)|Exercise SET-3Match The Following|2 Videos

  • LIMITS AND CONTINUITY

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise 1B( One Sided Limits)|71 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) (SET - 4)|5 Videos

  • LINEAR PROGRAMMING [APPENDIX-2]

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise -1|33 Videos

Similar Questions

Explore conceptually related problems

y=f(x) =x/(1+|x|), x in R, y in R is

If f : R to R such that f(x- f(y)) = f( f(y) ) + x f (y) +f(x) - 1 AA , y in R then f(x) is

If f : R to R is defined as f (x+ y) = f (x) + f (y) AA x, y in R and f (1) = 7, then find sum _(r =1) ^(n) f (r).

If f(x) satisfies the relation f(x+ y) = f ( x) + f( y ) for all x, y in R and f(1) = 5 then

f: R^(+) rarr R is continuous function satisfying f(x/y)=f(x) - f (y) AA x, y in R^(+) . If f'(1) = 1, then

If 'f is a function such that f (x + y) =f (x) f (y) for all x,y in R and f ^(1) (0) exists, show that f ^(1) (x) = f(x) f ^(1)(0) for all x, y in R.

Let f be a non zero continuous function satisfying f(x+y)=f(x) f(y) for all x, y in R . If f(2)=9 then f(3) is

If satisfies the relation f(x+y)+f(x-y)=2 " " f(x).f(y) AA x , y in R and f(0) != 0 , then f(10)-f(-10)=

DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. The value of f(0) so that f(x)=(log(1+x//a)-log(1-x//b))/(x) is contin...

    Text Solution

    |

  2. Let f(x)=(log(1+x+x^(2))+log(1-x+x^(2))/(sec x-cos x),x ne 0. Then the...

    Text Solution

    |

  3. The value of f(0) so that f(x)=((4^(x)-1)^(3))/(sin(x//4)log(1+x^(2)//...

    Text Solution

    |

  4. If f(x)=((a^(x)-1)^(3))/(sin (x log a)log (1+x^(2) log a^(2)) is conti...

    Text Solution

    |

  5. If If {{:(,(72^(x)-9^(x)-8^(x)+1)/(sqrt2-sqrt(1+cosx)),x ne 0),(,k log...

    Text Solution

    |

  6. If f : R to R is continuous such that f(x + y) = f(x) + f(y) x i...

    Text Solution

    |

  7. Let f be a non zero continuous function satisfying f(x+y)=f(x) f(y) fo...

    Text Solution

    |

  8. Given that the function f defined by f(x)={{:(,2x-1,"if "x gt 2),(,k,"...

    Text Solution

    |

  9. f(x) = (x^(3) + x^(2) - 16 x + 20)/((x - 2)^(2)) " if " x ne 2 , = k ...

    Text Solution

    |

  10. If f(x)=(x^(2)-10x+25)/(x^(2)-7x+10)"for "x ne 5 and f is continuous a...

    Text Solution

    |

  11. Let f(x) = (x + x^(2) + ...+ x^(n)-n)/(x -1), x ne 1, the value of f (...

    Text Solution

    |

  12. If the function f(x)=(sin 3x)/(x)" for "x ne 0 and f(0)=k/2 is continu...

    Text Solution

    |

  13. If f(x)={{:((sqrt(1+kx)-sqrt1-kx)/(x),"for" -1 le x0),(2x^(2)+3x-2,"fo...

    Text Solution

    |

  14. If : [ -2 ,2 ] to R is defined by f(x) = {: { ((sqrt(1+cx) -sqr...

    Text Solution

    |

  15. Let f(x)=-2 sin x, if x le (-pi)/(2), f(x)=a sin x+b," if "(-pi)/(2), ...

    Text Solution

    |

  16. If [x] denotes the greatest integer not exceeding x and if the functi...

    Text Solution

    |

  17. The values of p and q for which the function f(x)={{:(,(sin(p+1)x+sinx...

    Text Solution

    |

  18. Let f: R to R is defined by f(x)= {{:(,alpha+(sin [x])/(x),if x gt 0),...

    Text Solution

    |

  19. If R rarr R b e defined f(x)={{:(a^(2)cos^(2) x+b^(2) sin^(2)x,if xle0...

    Text Solution

    |

  20. f : R - {0} to R " given by " f(x) = (1)/(x) - (2)/(e^(2x)-1) can b...

    Text Solution

    |