Can the Inverse Function of f(x) = 2x + ln x Be Solved Algebraically?

[reza]

f(x) =2x + ln x
f^-1(x)=?


i do
f(x)=2x +lnx=ln (e^2x) + ln x = ln [(e^2x)x]
=>e^f(x)=e^2x(x)=>
can eny body solve this equation

 

[lalbatros]

There is no simple closed form for this inverse function.
But there are many ways to calculate numerical values of this function.
It is also possible to analyse it in great details, same job actually as for f, just reading in the reverse direction!
If you are familiar with that, it might be possible to make a series expansion for it.

Now, why would you need the inverse function explicitely?