f(x)=e^x-1+2x-3

and the question is

inverted function of x (f^-1(x))=0

please answer with steps

Guest Jul 9, 2015

#1**+5 **

$$\\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

Melody Jul 10, 2015