# inverse function

• Jan 15th 2008, 12:52 PM
rlarach
inverse function
12. Find the inverse function of g(x) = ln(x^3)
• Jan 15th 2008, 01:34 PM
Pinsky
I'm not totally sure if this is the correct solution for solving this, but here it goes.

$\displaystyle y=\ln{x^3}$
Then change the variables
$\displaystyle x=ln{y^3}$

and after that you get y.

$\displaystyle e^x=y^3$

$\displaystyle y=\sqrt[3]{x}$

Hope i didn't mix this with something else. (Tmi)
• Jan 15th 2008, 01:38 PM
mr fantastic
Quote:

Originally Posted by Pinsky
I'm not totally sure if this is the correct solution for solving this, but here it goes.

$\displaystyle y=\ln{x^3}$
Then change the variables
$\displaystyle x=ln{y^3}$

and after that you get y.

$\displaystyle e^x=y^3$

$\displaystyle y=\sqrt[3]{x}$ *

Hope i didn't mix this with something else. (Tmi)

All good 'til the line marked *

Should be $\displaystyle y=\sqrt[3]{e^x}$

$\displaystyle = e^\frac{x}{3}$
• Jan 15th 2008, 01:54 PM
Pinsky
Right, typing error, tnx.

Had an exam in line,surface and triple integrals..

Still waiting for the results thou. (Worried)