1. ## inverse function

If $f(x)=2x+ln x$, find $f^{-1}(2)$.
I keep getting stuck trying to get the inverse. Here's what i got:
$y=2x+lnx$
$-e^{lnx}+e^y=e^{2x}$
$-x+e^y=e^{2x}$
Then i don't know what to do, and i feel like i'm approaching it incorrectly.
So, i tried: $\frac{y}{2x}=lnx$
$x=e^{\frac{y}{2x}}$ and i'm still not getting anywhere.
Any help would be mucho appriciated!

2. Originally Posted by windir
If $f(x)=2x+ln x$, find $f^{-1}(2)$.
I keep getting stuck trying to get the inverse. Here's what i got:
$y=2x+lnx$
$\color{red}-e^{lnx}+e^y=e^{2x}$
$-x+e^y=e^{2x}$
Then i don't know what to do, and i feel like i'm approaching it incorrectly.
So, i tried: $\frac{y}{2x}=lnx$
$x=e^{\frac{y}{2x}}$ and i'm still not getting anywhere.
Any help would be mucho appriciated!
by inspection, $f^{-1}(2) = 1$ since $f(1) = 2(1) + \ln 1 = 2 + 0 = 2$

(by the way, what you did is incorrect. from the line in red)

3. ah thank you! obvious stuff usually trips me up!

4. Originally Posted by windir
ah thank you! obvious stuff usually trips me up!
you'd be surprised how common this vice is. take care.