Home
Class 12
MATHS
Let f: X -> Ybe an invertible function....

Let `f: X -> Y`be an invertible function. Show that the inverse of `f^(-1)`is f, i.e., `(f^(-1))^(-1)= f`.

A

`[pi/4,(5pi)/4] rarr [sqrt(2),3sqrt(2)]`

B

`[-pi/4,(3pi)/4] rarr [sqrt(2),3sqrt(2)]`

C

`[-(3pi)/4,(3pi)/4] rarr [sqrt(2),-3sqrt(2)]`

D

`[-(3pi)/4,-pi/4] rarr [sqrt(2),3sqrt(2)]`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 12|4 Videos
  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f be an invertible function.Show that the inverse of f^(-1) is f

Let f:X rarr Y be an invertible function.Show that the inverse of is f,i.e.,(f^(-1))^(-1)=f

Let f: X->Y be an invertible function. Show that f has unique inverse. (Hint: suppose g_1(" and g")_2 are two inverses of f. Then for all y in Y ,""""fog_1(y)=I_Y(y)=fog_2(y) Use one oneness of f ).

Let f : R to R : f(x) =(2x-7)/(4) be an invertible function . Find f^(-1)

Let f : R rarr R : f(x) = (2x-3)/(4) be an invertible function. Find f^(-1) .

Let f(x)=e^(x^(3)-x^(2)+x) be an invertible function such that f^(-1)=g ,then-

Let f:A rarr B be an invertible function.If f(x)=2x^(3)+3x^(2)+x-1, then f^(-1)(5)=

Let f (x) be invertible function and let f ^(-1) (x) be is inverse. Let equation f (f ^(-1) (x)) =f ^(-1)(x) has two real roots alpha and beta (with in domain of f(x)), then :

Let f be an invertible real function. Write (f^(-1)\ of)(1)+(f^(-1)\ of)(2)++(f^(-1)\ of)(100)dot

ARIHANT MATHS-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. Total number of values of x, of the form 1/n, n in N in the interval ...

    Text Solution

    |

  2. The sum of the maximum and minimum values of the function f(x)=1/(1+(2...

    Text Solution

    |

  3. Let f: X -> Ybe an invertible function. Show that the inverse of f^(-...

    Text Solution

    |

  4. The range of values of a so that all the roots of the equations 2x^(3)...

    Text Solution

    |

  5. If f(x) is continuous such that abs(f(x)) le 1, forall x in R " and " ...

    Text Solution

    |

  6. Let f(x)=sqrt(|x|-{x}), where {.} denotes the fractional part of x an ...

    Text Solution

    |

  7. If the graphs of the functionsy= log (e)x and y = ax intersect at exac...

    Text Solution

    |

  8. A quadratic polynominal maps from [-2,3] onto [0,3] and touches X-axis...

    Text Solution

    |

  9. The range of the function y=sqrt(2{x}-{x}^2-3/4) (where, denotes the f...

    Text Solution

    |

  10. Let f(x) be a fourth differentiable function such f(2x^2-1)=2xf(x)AA x...

    Text Solution

    |

  11. The number of solutions of the equation [y+[y]]=2 cosx, where y=(1)...

    Text Solution

    |

  12. If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x), then period of f(x)...

    Text Solution

    |

  13. If x and alpha are real, then the inequation log(2)x+log(x)2+2cos al...

    Text Solution

    |

  14. The range of values of ‘a' such that (1/2)^|x|= x² - a is satisfied f...

    Text Solution

    |

  15. Let f:R rarr R be a function defined by f(x)={abs(cosx)}, where {x} re...

    Text Solution

    |

  16. The domain of the function f(x)=sqrt(log(sinx+cosx)(abs(cosx)+cosx))...

    Text Solution

    |

  17. If f(x)=(x^(2)+2alphax+alpha^(2)-1)^(1//4) has its domain and range su...

    Text Solution

    |

  18. If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is -

    Text Solution

    |

  19. The expression x^2-4px+q^2> 0 for all real x and also r^2+ p^2 < qr t...

    Text Solution

    |

  20. Let f(x)=(x^(4)-lambdax^(3)-3x^(2)+3lambdax)/(x-lambda). If range of f...

    Text Solution

    |