Inverse of f(x)=e^x + e^-x+1

[Eishan M]

Hi,
What is the inverse of f(x)= e^x + e^-x +1?

 

[Eishan M]

This question has been intimidating me for quite a while. I'm unable to reach a definite conclusion to this. Please help

 

[Hawkeye18]

Try solving $$e^x+e^{-x}+1=y.$$

 

[mathman]

Convert problem into a quadratic equation by $u=e^x,\ u^2+1+u(1-y)=0$. Get u as a function of y, then x=ln(u).