Home
Class 12
MATHS
Prove that the function f:N to Y d...

Prove that the function `f:N to Y ` defined by ` f(x) = 4x +3 ,` where ` Y=[y:y =4x +3,x in N]` is invertible . Also write inverse of f(x).

Text Solution

Verified by Experts

The correct Answer is:
`(x-3)/4`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ANNUAL EXAM QUESTION PAPER MARCH -2014

    SUNSTAR PUBLICATION|Exercise PART-E|4 Videos

  • ANNUAL EXAM QUESTION PAPER MARCH -2014

    SUNSTAR PUBLICATION|Exercise PART-C|14 Videos

  • ANNUAL EXAM QUESTION PAPER MARCH - 2016

    SUNSTAR PUBLICATION|Exercise PART - E (Answer any one questions)|8 Videos

  • II PUC MATHEMATICS ( SUPPLEMENTARY EXAM QUESTION PAPER JUNE -2019)

    SUNSTAR PUBLICATION|Exercise PART-E|3 Videos

Similar Questions

Explore conceptually related problems

Prove that the function f: N to Y defined by f(x) = x^(2) , where y = {y : y = x^(2) , x in N} is invertible. Also write the inverse of f(x).

Verify whether the function f : N to Y defined by f(x) = 4x + 3 , where Y = {y : y = 4x + 3, x in N} is invertible or not. Write the inverse of f(x) if exists.

Knowledge Check

  • Let f:NtoY be a function defined as f(x)=4x+3 , where Y={yinN,y=4x+3 for some x inN }. Show that f is invertible and its inverse is :

    A
    `g(y)=(y-3)/(4)`
    B
    `g(y)=(3y+4)/(3)`
    C
    `g(y)=4+(y+3)/(4)`
    D
    `g(y)=(y+3)/(4)`

    • Similar Questions

    Explore conceptually related problems

    Prove that the function f : R to R defined by f(x) = 3 - 4x , AA x in R is bijective.

    Prove that the function f: R to R defined by f(x) = 4x + 3 is invertible and find the inverse of 'f' .

    Prove that the funciton f: R to R defined by f(x)=4x+3 is invertible and find the inverse of f.

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

    Let f : N to R be defined by f(x) = 4x^(2) + 12x + 15 , show that f: N to S , where S is the function, is invertible. Also find the inverse.

    Let R+ be the set of all non-negative real number. Show that the faction f : R, to [4, oo) defined f(x) = x^(2) + 4 is invertible. Also write the inverse of f.

    Show that the function f : N to N defined by f(x) = x^(3), AA x in N is injective but not surjective.

    Home
    Profile