Question

How can I find the inverse function of

f(x) = e^x^3 ??

Answer 1

I know that I have to switch places of 'x' and 'y' and then solve for 'y'. But I need help to solve for 'y' in this case.

Answer 2

x=e^y^3

Answer 3

so that's a good start

\[x = e^{y^3}\]

any thoughts on the next step..?

Answer 4

hint... it involves logs...

Answer 5

Right, so do we have to take log on both sides?

Answer 6

correct... use natural logs

and uses the log law

\[\ln(e^a) = a\]

so

\[\ln(x) = y^3\]

can you finish from here..?

Answer 7

Ohhh got it!! Yeah I can take it from here :D Thank you soooo much! I always get confused when it comes to logs >.<

Answer 8

glad to help...

Answer 9

Thanks :)