Question

Consider $f:R\to R$ given by $f\left(x\right)=2x+3$. Show that f is invertible. Find also the inverse of function f.

Answer 1

$f\left(x\right)=2x+3$

$\Rightarrow y=2x+3$

To find its inverse,

$y-3=2x$

$\Rightarrow x=\frac{y-3}{2}$

Therefore the inverse is:

$f^{-1}\left(x\right)=\frac{x-3}{2}$