inverse function

**windir** · January 24th 2010, 10:42 PM

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!

**Jhevon** · January 24th 2010, 10:57 PM

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)

**windir** · January 24th 2010, 11:26 PM

ah thank you! obvious stuff usually trips me up!

**Jhevon** · January 24th 2010, 11:30 PM

Originally Posted by windir

ah thank you! obvious stuff usually trips me up!

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

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