Inverted function

hi anon,

This is an inverse function question                   (Factorials are something completely different)

$$\\f(x)=e^x-1+2x-3\\\\
Let\;\; y=f(x)\\
y=e^x-1+2x-3\\
y=e^x+2x-4\\
Domain\;\;x\in R \;\;and \;\; range\;\;y\in R\\
$and both x and y are both mapped 1 to 1 to the other$\\
$So it is ok for me to just going to swap x and y over$\\
$the inverse function is $\\
x=e^y+2y-4\\
If \;\;y=0\;\; then\;\; x=e^0+2*0-4=1-4=-3$$

 $$\\f^{-1}(x)=0 \qquad when \qquad x=-3$$

Here is the graph

https://www.desmos.com/calculator/lb12iqyjf0

Thanks a lot.Now I know how to solve equations with inverted factorial.I wish you the best!