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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`

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The correct Answer is:
`f^(-1)(x)=(x-3)/(4)`
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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.

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).

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)`

  • The lines (x-1)/2=(y-2)/4=(z-3)/7 and (x-1)/4 =(y-2)/5=(z-3)/7 are :

    A
    perpendicular
    B
    intersecting
    C
    skew
    D
    parallel

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

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

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    Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 .

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