Home
Class 12
MATHS
Let f:WrarrW be defined as f(n) = n-1 i...

Let `f:WrarrW` be defined as f(n) = n-1 if n is odd and
f(n) = n+1 if n is even.
Show that f is invertible. Find the inverse of f. Here W is the set of all whole numbers.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|86 Videos

  • PROBABILITY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|318 Videos

  • THREE DIMENSTIONAL GEOMETRY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|97 Videos

Similar Questions

Explore conceptually related problems

Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.

Consider f:RtoR given by f(x)=3x+2 show that f is invertible. Find the inverse of f

Let N rarr R be a function defined as f(x) = 4x^2 + 12x +15 Show that f : N rarr S , where, S is the range of f, is invertible. Find the inverse of f.

if f(x)=x/(x-1) , x!=1 find the inverse of f

Let f: N to N be defined by f(n) = { (((n+1)/2)if n is odd), (n/2 if n is even) :} for all n in N State whether the function f is bijective. Justify yur answer.

Let f:RtoR be given by f(x)=frac(2x+1)(3) find fof and show that f is invertible.

Show that f : N rarr N given by f(x) = { ((x +1), if x is odd), ((x - 1), if x is even) :} is both one-one and onto.

Let f : X rarr Y be invertible, show that f has unique inverse

If f: N rarr Z is defined by f(n) ={{:((n-1)/(2),"when n is odd"),(-n/2,"when n is even"):} then identify the type of function

A N EXCEL PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Consider an operation ** defined on the set A={1,2,4,8} by a**b=LCM ...

    Text Solution

    |

  2. Let ast be a binary operation on N defined by aastb=HCF of a and b I...

    Text Solution

    |

  3. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  4. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  5. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  6. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  7. Consider the binary operation ast on the set R of real numbers, define...

    Text Solution

    |

  8. Determine whether or not each of the definitions of ** given below giv...

    Text Solution

    |

  9. Find which of the following of the operations given above has identity...

    Text Solution

    |

  10. Find which of the following of the operations given above has identity...

    Text Solution

    |

  11. Find which of the following of the operations given above has identity...

    Text Solution

    |

  12. Find which of the following of the operations given above has identity...

    Text Solution

    |

  13. Let ** be a binary operation on the set Z of integers as a**b=a+b+1. T...

    Text Solution

    |

  14. Let A=NtimesN and ast be a binary operation on A defined by (a,b)...

    Text Solution

    |

  15. State whether the following statements are true or false. Justify For...

    Text Solution

    |

  16. State whether the following statements are true or false. Justify If ...

    Text Solution

    |

  17. Consider a binary operation ** on N defined as a**b=a^3+b^3. Choose th...

    Text Solution

    |

  18. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

    Text Solution

    |

  19. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 if...

    Text Solution

    |

  20. If f:RrarrR is defined by f(x) = x^2-3x+2, find f(f(x))

    Text Solution

    |