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

To show that the function \( f: \mathbb{N} \to Y \) defined by \( f(x) = 4x + 3 \) is invertible, we need to find its inverse function \( g \) and verify that \( g(f(x)) = x \) and \( f(g(y)) = y \).

### Step 1: Define the function
The function is given as:
\[ f(x) = 4x + 3 \]
where \( Y = \{ y \in \mathbb{N} : y = 4x + 3 \text{ for some } x \in \mathbb{N} \} \).
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