Let $f:N\to Y$  be a function defined as $f\left(x\right)=4x+3$ , where $Y=\left\{y\in N;y=4x+3forsomex\in N\right\}$ , show that $f$  is invertible and its inverse is

$f\left(x\right)=4x+3,f:N\to Y,Y$ $=\left\{y\in N:y=4x+3,x\in N\right\}$

$\therefore$  $Y$  is range of $f$

Also, clearly,$f$  is one-one, so $f$  is invertible.

$\Rightarrow y=f\left(x\right)=4x+3\Rightarrow x=f^{-1}\left(y\right)$ $=\frac{y-3}{4}$

Hence, $f^{-1}\left(y\right)=g\left(y\right)$ $=\frac{y-3}{4}$ .