Home
Class 12
MATHS
If f(x) is continuous such that abs(f(x)...

If f(x) is continuous such that `abs(f(x)) le 1, forall x in R " and " g(x)=(e^(f(x))-e^(-abs(f(x))))/(e^(f(x))+e^(-abs(f(x)))),` then range of g(x) is

A

`[0,1]`

B

`[0, (e ^(2)+1)/(e ^(2)-1)]`

C

`[0, (e ^(2)-1)/(e ^(2)+1)]`

D

`[ (e ^(2)+1)/(e ^(2)+1),0]`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VK JAISWAL|Exercise ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT|25 Videos

  • FUNCTION

    VK JAISWAL|Exercise COMPREHENSION TYPE PROBLEMS|15 Videos

  • ELLIPSE

    VK JAISWAL|Exercise Exercise-4 : Subjective Type Problems|2 Videos

  • HYPERBOLA

    VK JAISWAL|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

If e^(x)+e^(f(x))=e then domain of f(x) is

If f(x)=(e^(x)+e^(-x))/(2) then inverse of f(x) is

abs(f(x)-f(y))le(x-y)^2 forall x,y in R and f(0)=1 then

If e ^(x)+e^(f(x))=e, then for f (x) domain is:

Let f:R rarr R" be defined by "f(x)=(e^(|x|)-e^(-x))/(e^(x)+e^(-x)). Then

Function f:R rarr R;f(x)=(e^(x^(2))-e^(-x^(2)))/(e^(x^(2))+e^(-x^(2))) is :

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

VK JAISWAL-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. If f(x) is continuous such that abs(f(x)) le 1, forall x in R " and " ...

    Text Solution

    |

  2. Let f(x) be a polynomial of degree 6 with leading coefficient 2009. Su...

    Text Solution

    |

  3. Let f (x) =x ^(3)-3x Find f (f (x))

    Text Solution

    |

  4. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

    Text Solution

    |

  5. If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...

    Text Solution

    |

  6. The number of elements in the range of functions: y=sin^(-1) [x^(2)+5/...

    Text Solution

    |

  7. The number of integers in the range of function f(x)= [sinx] + [cosx] ...

    Text Solution

    |

  8. If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...

    Text Solution

    |

  9. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

    Text Solution

    |

  10. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

    Text Solution

    |

  11. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

    Text Solution

    |

  12. Find the number of elements contained in the range of the function f (...

    Text Solution

    |

  13. Let f (x,y)= x^(2) - y^(2) and g (x,y) = 2xy. such that (f ( x,y))^(2)...

    Text Solution

    |

  14. Let f (x) = (x+5)/(sqrt(x^(2)) +1) AA x in R, then the smallest integr...

    Text Solution

    |

  15. The number of integral vaues of which f : R to R ,f (x) = (x ^(2))/(3)...

    Text Solution

    |

  16. The number of roots of equation ((x-1)(x-3))/((x-2)(x-4))-e^(x)) ((x+1...

    Text Solution

    |

  17. Let f(x)=x^2-bx+c,b is an odd positive integer. Given that f(x)=0 ha...

    Text Solution

    |

  18. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  19. If f (x) = 4x ^(3) -x ^(2) -2x +1 and g (x) = {{:(min {f(t): 0 le t le...

    Text Solution

    |

  20. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  21. Let f x = (ax+b)/(xa+d), where a,b,c d are non zero If f (7) =7,f (11)...

    Text Solution

    |