## owlet one year ago Domain of the inverse help! The function is f(x)=ln(e^y - 3).

1. owlet

|dw:1443324096677:dw|

2. anonymous

Ok so this is a one-to-one function

3. owlet

|dw:1443324955839:dw| this is what i got.. am i right?

4. anonymous

$f(x) = \ln(e^x-3)$$y=\ln(e^x-3)$$x=\ln(e^y-3)$$\large e^x =e^{\ln_e(e^y-3)}$$e^x =e^y-3$$e^y=e^x+3$$\ln (e^y) = \ln(e^x+3)$$y=\ln(e^x+3)$ This is what I'm getting.

5. anonymous

$\huge \checkmark$

6. owlet

oh yeah i have to use ln not log :3 thanks!

7. anonymous

Uhh... not entirely.

8. anonymous

$\color{red}{\log_e (x) \equiv \ln(x)}$

9. owlet

??

10. anonymous

Either you write your inverse as a log based function, which entails it has a base of e, or you take the natural log function which works off base e as well, theyre equivalent

11. owlet

yeah, so if I write it in terms of log, it will be like: |dw:1443325371555:dw|

12. anonymous

Yes

13. owlet

yay, thank you so much!

14. anonymous

For practice, you should try this problem: $$\large f(x) =\dfrac{e^{2x}-1}{2-e^2x}$$

15. anonymous

$\large f(x) = \frac{e^{2x}-1}{2-e^{2x}}$

16. owlet

ok, I will also find the inverse of that function?

17. anonymous

Yeah. It'll help you practice how to find inverse of logarithmic functions

18. owlet

ok..|dw:1443325598398:dw||dw:1443325667079:dw| Can I simplify it more?

19. owlet

wait i think i did something wrong..

20. owlet

no i think i'm right :P |dw:1443326011460:dw|