Home
Class 12
MATHS
The function f : R//{0} rarr R given by ...

The function `f : R//{0} rarr R` given by :
`f(x) = (1)/(x) - (2)/(e^(2x) - 1)` can be made continuous at x = 0 by defining f(0) as :

A

0

B

1

C

2

D

(-1)

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

The function f : R rarr R defined by f(x) = 7^x + 7^|x| is

If the function f : R rarr A given by f(x) = (x^2)/(x^2+1) is a surjective then A =

Let, f : R rarr R be given by f(x) = tan x . Then f^-1(1) =

If f: R rarr R is defined by f(x)=(x)/(x^(2)+1) find f(f(2))

Let f: R rarr R be given by f(x)=(x+1)^(2)-1, x ge-1 . Then f^(-1)(x)=

The inverse of the function f: R rarr R given by f(x) = log_{a}(x+sqrt(x^2+1)(a gt 0, a ne 1) is

The inverse of function f:R rarr { x in R : x lt 1} given by f(x) = (e^x-e^-x)/(e^x+e^-x) is

If f : R rarr R is defined by f(x) = {((cos3x-cosx)/x^(2), x ne 0),(lambda, x = 0):} and if f is continuous at x = 0 then lambda is equal to

If f : R to R is defined by f(x) = x/(x^(2)+1) find f(f(2)) .

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Which of the following function is differentiable at x=0?

    Text Solution

    |

  2. Let f(x) = (1-tanx)/(4x-pi),x ne (pi)/(4), x in [0, (pi)/(2)], if f(x)...

    Text Solution

    |

  3. The function f : R//{0} rarr R given by : f(x) = (1)/(x) - (2)/(e^(2...

    Text Solution

    |

  4. If f : R rarr R is defined by f(x) = {((cos3x-cosx)/x^(2), x ne 0),(la...

    Text Solution

    |

  5. f(x) = (sqrt(1+px) - sqrt(1 - px))/(x), -1 le x le 0 = (2x + 1)/(x-2),...

    Text Solution

    |

  6. Let f(x) = {(x^(4)-5x^(2)+4)/(|(x-1)(x-2)|) x ne 1,2),(6, x=1), (12, x...

    Text Solution

    |

  7. Let f(x) = (1-sin x)/((pi - 2x)^(2)),"where x" ne pi//2 and f(pi//2) =...

    Text Solution

    |

  8. The value of f(0) so that the function f(x) = ((27-2x)^(1/3)-3)/(9-3(2...

    Text Solution

    |

  9. Let f(x) = {((tanx - cotx)/(x-pi/4), xne pi/4),(a, x = pi/4):}. The va...

    Text Solution

    |

  10. The value of f(0), so that the function f(x) = (sqrt(a^(2)-ax+x^(2))-s...

    Text Solution

    |

  11. The function f(x)=1+|sinx| is :

    Text Solution

    |

  12. The range of the function f(x)=[x]-x , where [x] denotes the greatest ...

    Text Solution

    |

  13. Let f((x+y)/2) = (f(x)+f(y))/2 for all real values of x and y. If f^('...

    Text Solution

    |

  14. Let f : R rarr R be a function defined by f(x) = max {x,x^(3)}. The se...

    Text Solution

    |

  15. The domain of the derivative of the function f(x) = {(tan^(-1)x, |x|le...

    Text Solution

    |

  16. lim(h rarr 0) (f(2h+2+h^(2))-f(2))/(f(h-h^(2)+1)-f(1)) given that f^('...

    Text Solution

    |

  17. If f(x) is differentiable increasing function, then lim(x to 0) (f(x^(...

    Text Solution

    |

  18. If f(x) is continuos and differentiable function such that f(1/n) = 0 ...

    Text Solution

    |

  19. Let f(x+y) = f(x).f(y), forall, x, y. Suppose f(5) =2, f^(')(0) = 3 th...

    Text Solution

    |

  20. If f(x) = {(x-5,x le1),(4x^(2)-9, 1ltxlt2),(3x+4, x ge2):} then f^(')(...

    Text Solution

    |