Home
Class 12
MATHS
Let f"":""NvecY be a function defined...

Let `f"":""NvecY` be a function defined as `f""(x)""=""4x""+""3` , where `Y""=""{y in N"":""y""=""4x""+""3` for some `x in N}` . Show that f is invertible and its inverse is (1) `g(y)=(3y+4)/3` (2) `g(y)=4+(y+3)/4` (3) `g(y)=(y+3)/4` (4) `g(y)=(y-3)/4`

Text Solution

Verified by Experts

The correct Answer is:
`I _(N)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.1|16 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

Let f:N rarr Y be a function defined as f(x) = 4x + 3, where, Y = { y in N:y = 4x + 3 for some x in N }. Show that f is invertible. Find the inverse.

Let f: R -{-4/3}rarrR be a function defined as f(x) =(4x)/(3x+4) . The inverse of f is the map g : Range f rarrR - {-4/3} given by

Let f(x, y) be a periodic function satisfying f(x, y) = f(2x + 2y, 2y-2x) for all x, y; Define g(x) = f(2^x,0) . Show that g(x) is a periodic function with period 12.

The angle "bet"^(n) two line ( x+3)/(3) = (y-1)/(5) = (z +3)/(4) and ( x+1)/(1) =(4-y)/(-1) =(z-5)/(2) is ……..

The angle "bet"^(n) two line ( x+3)/(3) = (y-1)/(5) = (z +3)/(4) and ( x+1)/(1) =(4-y)/(-1) =(z-5)/(2) is ……..

Find differentiation of y w.r.t x. (i) y=(sin x)/x , (ii) y=(4x^(3))/e^(x)

Expand : (4x-y)^(3)

Find dervatives of the following functions: (i) y=2x^(3) , (ii) y=4/x , (iii) y=3e^(x) , (iv) y=6 ln x , (v) y=5 sin x

NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , wher...

    Text Solution

    |

  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

  3. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

    Text Solution

    |

  4. If f:R to R is defined by f(x) = x^(2)-3x+2, write f{f(x)}.

    Text Solution

    |

  5. Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...

    Text Solution

    |

  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  9. Given a non-empty set X , consider P\ (X) which is the set of all subj...

    Text Solution

    |

  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  11. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  13. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

    Text Solution

    |

  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  15. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

    Text Solution

    |

  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |