Home
Class 12
MATHS
Let f: R to R be a function such that f...

Let `f: R to R` be a function such that `f(x+y) = f(x) + f(y) AA x, y in R`. If If f(x) is differentiable at x = 0, then

A

f(x) is differentiable only in a finite interval containing 0

B

f(x) is continuous `AA x in R`

C

`f'(x)` is constant `AA x in R`

D

f[x) is differentiable except at finitely many points

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise SELF ASSESSMENT TEST (TRUE AND FALSE TYPE QUESTIONS) |1 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise SELF ASSESSMENT TEST (FILL IN THE BLANKS) |4 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (5) (MULTIPLE CHOICE QUESTIONS) |12 Videos

  • INVERSE CIRCULAR FUNCTIONS

    ML KHANNA|Exercise Self Assessment Test|25 Videos

  • LINEAR PROGRAMMING

    ML KHANNA|Exercise Self Assessment Test|8 Videos

Similar Questions

Explore conceptually related problems

Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in R. If f (x) is differentiable at x = 0, then

If y= f (x) is differentiable AA x in R, then

Let f:R to R be a function such that f(x+y)=f(x)+f(y)"for all", x,y in R If f(x) is differentiable at x=0. then, which one of the following is incorrect?

Let f:R rarr R be a function such that f(x+y)=f(x)+f(y),AA x,y 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

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f be a polynominal such that f(x) f(y) + 2 = f(x) + f(y) + f(xy) AA xx, y in R (0) and f(x) is one one AA xx in R with f(0) = 1 and f (1) = 2 The function y = f(x) is given by

If f:R rarr R be a function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y and f(2) = 4 then, f(1)-f(0) is equal to

ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)
  1. The function f (x) = 1+ |sin x| is

    Text Solution

    |

  2. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

    Text Solution

    |

  3. The following functions are continuous on (0, pi)

    Text Solution

    |

  4. If f (x) = 1/2 x - 1, then on the interval [0, pi]

    Text Solution

    |

  5. If f(x) = 3x-5, then f^(-1) (x)

    Text Solution

    |

  6. If underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) the...

    Text Solution

    |

  7. Show that the underset(xto2)lim((sqrt(1-cos{2(x-2)}))/(x-2)) doesnot e...

    Text Solution

    |

  8. Let f: R to R be a positive increasing function with lim(x to infty) (...

    Text Solution

    |

  9. If underset(x to infty)lim((x^(2)+x+1)/(x+1)-ax -b)=4 then

    Text Solution

    |

  10. The value of p and q for which the function f(x) = {((sin(p+1)x+sinx...

    Text Solution

    |

  11. Let f : (-1,1) to R be a differentiabale function with f(0) = -1 and f...

    Text Solution

    |

  12. If f: R to R is a function defined by f(x) = [x] cos((2...

    Text Solution

    |

  13. Let L= lim(x to 0)(a- sqrt(a^(2)-x^(2))-x^(2)/4)/x^(4), a gt 0. If L i...

    Text Solution

    |

  14. Let f: R to R be a function such that f(x+y) = f(x) + f(y) AA x, y in...

    Text Solution

    |

  15. If f(x) = {{:(-x-pi/2" , " x le - pi/2),(-cos x" , " -pi/2 lt ...

    Text Solution

    |

  16. Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constan...

    Text Solution

    |

  17. Let f be a real valued function defined on the interval [0,infty] by f...

    Text Solution

    |

  18. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  19. Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...

    Text Solution

    |

  20. Let f(x)={x^2 |cospi/x|, ,x !=0, x in R, x=0 then f is

    Text Solution

    |