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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).

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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).

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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)`

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