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`

Explanation

`f:N → Y f(x) = 4x + 3`

Let `f(x_1) = f(x_2)`

`4x_1 + 3 = 4x_2 + 3`

`4x_1 = 4x_2`

∴ `x_1 = x_2`

∴ `f` is one - one

To prove that f is onto
Let y ∈ Y there exits x ∈ N such that
`f(x) = y`

`4x + 3 = y`

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