Let $f:N\to Y$ be a function defined as $f\left(x\right)=4x+3$ where $Y=\left\{y\in N: y=4x+3for some x\in N\right\}$ then the inverse of the function $f\left(x\right)$ is 

The given function is $f\left(x\right)=4x+3$

suppose that 

          $\begin{array}{rcl}y& =& 4x+3\\ y-3& =& 4x\\ x& =& \frac{y-3}{4}\end{array}$

Therefore, the invere function of $f\left(x\right)=4x+3$ is $g\left(y\right)=\boxed{\frac{y-3}{4}}$