Can't find solution derivative of inverse function problem! I am completely stuck on this problem. 
It reads: 
If $g$ is the inverse function of $f(x) = 2x + ln(x)$ , find $g'(2)$. 
I know that $g'(a) = 1 / f'( g(a) )$ 
I've tried this a whole bunch of ways. I can't find $g(x)$ and I tried to use the online inverse function calculators to find it and they don't have a solution either! This means I can't find $g(2)$. 
My calculus book has given me several problems where I can't seem to find the inverse. So how am I supposed to use that formula?
My only other idea was to use linear algebra. As in find the tangent line at $(f(x), x)$ and reflect about $y = x$. But I still can't find  $x$! 

Use the formula. 
$$
g'(2)=\frac{1}{f'(g(2))}
$$
Hopefully you can find what $f'$ is. To find $g(2)$, let $c=g(2)$ and since $g$ is the inverse of $f$, we have that
$$
2c+\ln c=f(c)=2
$$
Clearly $c=1$ is a solution. To argue that it is unique observe that $f$ is strictly increasing.
