Home
Class 12
MATHS
Let f:NrarrY, be a function defined as f...

Let `f:NrarrY, 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.

Text Solution

Verified by Experts

The correct Answer is:
`(x-3)/4`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS )|8 Videos

  • PROBABILITY

    BETTER CHOICE PUBLICATION|Exercise Previous year Board.s questions for practice|43 Videos

  • THREE DIMENSIONAL GEOMETRY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE |60 Videos

Similar Questions

Explore conceptually related problems

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

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.

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

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

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

Let f: NrarrR , be a function defined as f (x) = 4x^2 + 12x + 15, forall x in N , show that f: NrarrS where S, is range of f is invertible.

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

Consider f: Rrarr [- 5, ∞) given by f(x) = 9x^2 + 6x- 5 . Show that f is invertible. Find the inverse of f.

BETTER CHOICE PUBLICATION-RELATIONS AND FUNCTIONS -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. If f : R rarr R defined by : f(x) = frac {3-2x}{4} is an inversible fu...

    Text Solution

    |

  2. If f : R rarr R defined by : f(x) = frac {6-5x}{7} is an inversible fu...

    Text Solution

    |

  3. Prove that the relation R in Z of integers given by: R = {(x, y): 2x -...

    Text Solution

    |

  4. Let f:NrarrY, be a function defined as f(x) = 4x+3, where, Y = {y in ...

    Text Solution

    |

  5. In a binary operation **: phi xx phi rarr phi is defined as a ** b = (...

    Text Solution

    |

  6. If f(x) = 4x – 1 and g(x)=x^3 + 2, find gof

    Text Solution

    |

  7. If f(x) = 4x – 1 and g(x)=x^3 + 2, find gof

    Text Solution

    |

  8. If f(x) = sin x and g(x) = 2x, find fog.

    Text Solution

    |

  9. Is f(x) = (x-1)/(x+1) invertible in its domain ? If so find, f^(-1) F...

    Text Solution

    |

  10. Consider f:R^(+) rarr [-5, oo] given by f (x) = 9x^(2) + 6x - 5 show ...

    Text Solution

    |

  11. If a**b=a/2+b/3 then find value of 2 ** 3.

    Text Solution

    |

  12. Show that the relation R in the set R of real number defined as R = {(...

    Text Solution

    |

  13. If R is the relation ‘lessthan from A={1,2,3,4,5} to B={1,4,5}. Write ...

    Text Solution

    |

  14. If R is the relation ‘less than' from set A = {1, 2, 3, 4, 5} to B = {...

    Text Solution

    |

  15. Show that R= {(a, b): a ge b} is reflexive and transitive but not sym...

    Text Solution

    |

  16. If f(x)= [x], g (x) = abs(x), then find the value of (fog) (5/2) - (go...

    Text Solution

    |

  17. If f:R rarr R is defined by f(x) = x^2 – 3x + 2, find f(f(x))

    Text Solution

    |

  18. Find gof and fog if : f(x) =|x| and g (x) = (5x-2)

    Text Solution

    |

  19. Show that relation R in Z of integers given by R = {x,y} : x - y is di...

    Text Solution

    |

  20. Show that f: Rrarr R defined by f(x)= (4x-3)/5 , "x" inR is invertib...

    Text Solution

    |