Home
Class 12
MATHS
Let f : R->R be a function defined by ...

Let `f : R->R` be a function defined by `f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x))` then --(1) f is bijection (2) f is an injection only (3) f is a surjection (4) f is neither injection nor a surjection

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

Let f:Rto R be a functino defined by f (x) = e ^(x) -e ^(-x), then f^(-1)(x)=

f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

If f: R->(0,\ 2) defined by f(x)=(e^x-e^(-x))/(e^x+e^(-x))+1 is invertible, find f^(-1)dot

If the function of f:R->A is given by f(x)=(e^x-e^(-|x|))/(e^x+e^(|x|)) is surjection, find A

If f:[0,oo[vecR is the function defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2), then check whether f(x) is injective or not.

The inverse of the function f:Rto range of f, defined by f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x)) is

Let f be a real valued function defined by f(x)=(e^x-e^(-|x|))/(e^x+e^(|x|)) , then the range of f(x) is: (a)R (b) [0,1] (c) [0,1) (d) [0,1/2)

Let f: RrarrR be defined by f(x)=(e^x-e^(-x))//2dot then find its inverse.

If f: R->R be the function defined by f(x)=4x^3+7 , show that f is a bijection.

Function defined by f(x) =(e^(x^(2))-e^(-x^(2)))/(e^(x^(2))+e^(-x^(2))) is injective in [alpha -2 ,oo) the least value of alpha is ____

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one...

    Text Solution

    |

  2. The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=sin^(-...

    Text Solution

    |

  3. Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(...

    Text Solution

    |

  4. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!...

    Text Solution

    |

  5. Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is...

    Text Solution

    |

  6. f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-on...

    Text Solution

    |

  7. The function f: R->R , f(x)=x^2 is (a) injective but not surjective (b...

    Text Solution

    |

  8. A function f from the set of natural numbers to integers defined by...

    Text Solution

    |

  9. Which of the following functions from A={x in R :-1lt=xlt=1} to its...

    Text Solution

    |

  10. Let f: Z->Z be given by f(x)={x/2,\ if\ x\ i s\ e v e n,0,\ if\ x\ i s...

    Text Solution

    |

  11. The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and on...

    Text Solution

    |

  12. Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation fo...

    Text Solution

    |

  13. If f(x)=3x-5, then f^(-1)(x) (a) is given by 1/((3x-5)) (b) is given...

    Text Solution

    |

  14. If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then (a).f(x)=sin^2x ,g...

    Text Solution

    |

  15. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  16. If the function f:(1,oo) vec (1,oo) is defined by f(x)=2^(x(x-1)),t h ...

    Text Solution

    |

  17. Let A={x in R : xlt=1} and f: A->A be defined as f(x)=x(2-x). Then, f...

    Text Solution

    |

  18. Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=(a) x for all x in R...

    Text Solution

    |

  19. If the function f: R->R be such that f(x) = x-[x], where [x] denotes t...

    Text Solution

    |

  20. If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals....

    Text Solution

    |