# inverse function

• Jan 24th 2010, 11:42 PM
windir
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!
• Jan 24th 2010, 11:57 PM
Jhevon
Quote:

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)
• Jan 25th 2010, 12:26 AM
windir
ah thank you! obvious stuff usually trips me up!
• Jan 25th 2010, 12:30 AM
Jhevon
Quote:

Originally Posted by windir
ah thank you! obvious stuff usually trips me up!

you'd be surprised how common this vice is. take care.