Home
Class 12
MATHS
Let Y = {n^2: n in N} in N. Consider ...

Let `Y = {n^2: n in N} in N`. Consider `f : N ->Y`as `f(n)=n^2`. Show that f is invertible. Find the inverse of f.

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: W ->W 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.

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

Let f: N -> S be a function defined as f(x)=9x^2+6x-5 . Show that f:N -> S, where S is the range of f , is invertible. Find the inverse of f and hence f^(-1)(43) and f^(-1)(163)

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

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.

Let f : N rarr N be a function defined as f(x) = 4x^(2) + 12x + 15 is invertible (where S is range of f). Find the inverse of f and hence find f^(-1)(31) .

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

Let A = {9, 10 , 11 , 12 , 13} and let f : A ->N be defined by f(n) = the highest prime factor of n. Find the range of f.

Let A = {9, 10 , 11 , 12 , 13} and let f : A ->N be defined by f(n) = the highest prime factor of n. Find the range of f.

Let A = {9, 10 , 11 , 12 , 13} and let f : A ->N be defined by f(n) = the highest prime factor of n. Find the range of f.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. The value of parameter alpha, for which the function f(x) = 1+alpha x,...

    Text Solution

    |

  2. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , wher...

    Text Solution

    |

  3. Let Y = {n^2: n in N} in N. Consider f : N ->Yas f(n)=n^2. Show tha...

    Text Solution

    |

  4. Let f : N ->Rbe a function defined as f(x)=4x^2+12 x+15. Show that f ...

    Text Solution

    |

  5. State with reason whether following functions have inverse (i) f:{1,2...

    Text Solution

    |

  6. State with reason whether following functions have inverse (i) f:{1,2...

    Text Solution

    |

  7. State with reasons whether h :{2,\ 3,\ 4,\ 5}->{7,\ 9,\ 11 ,\ 13} wi...

    Text Solution

    |

  8. Find f^(-1) if it exists: f: A->B where A={0,\ -1,\ -3,\ 2}; B= {-9,\ ...

    Text Solution

    |

  9. Find f^(-1) if it exists: f: A->B where A={1,\ 3,\ 5,\ 7,\ 9}; B= {0,\...

    Text Solution

    |

  10. Consider f:{1,\ 2,\ 3}->{a ,\ b ,\ c} and g:{a ,\ b ,\ c}-> {apple, ba...

    Text Solution

    |

  11. Let A={1,2,\ 3,\ 4};\ B={3,\ 5,\ 7,\ 9}; C={7,\ 23 ,\ 47 ,\ 79} and f:...

    Text Solution

    |

  12. Show that the function f: Q->Q defined by f(x)=3x+5 is invertible. Als...

    Text Solution

    |

  13. Consider f: R->Rgiven by f(x) = 4x + 3. Show that f is invertible. Fin...

    Text Solution

    |

  14. Consider f\ : R+vec[4,oo) given by f(x)=x^2+4 . Show that f is inve...

    Text Solution

    |

  15. If f(x)=(4x+3)/(6x-4),\ x\ !=2/3, show that fof(x)=x for all x!=2/3dot...

    Text Solution

    |

  16. Consider f: R+->[-5,oo)given by f(x)=9x^2+6x-5. Show that f is inverti...

    Text Solution

    |

  17. If f: R->R be defined by f(x)=x^3-3 , then prove that f^(-1) exists an...

    Text Solution

    |

  18. A function f: R->R is defined as f(x)=x^3+4 . Is it a bijection or not...

    Text Solution

    |

  19. If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=...

    Text Solution

    |

  20. Let A=R-{3}a n dB=R-{1}dot Consider the function f: Avec defined by f(...

    Text Solution

    |