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

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Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Ok so this is a onetoone function

owlet
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443324955839:dw this is what i got.. am i right?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[f(x) = \ln(e^x3) \]\[y=\ln(e^x3)\]\[x=\ln(e^y3)\]\[\large e^x =e^{\ln_e(e^y3)}\]\[e^x =e^y3\]\[e^y=e^x+3\]\[\ln (e^y) = \ln(e^x+3)\]\[y=\ln(e^x+3)\] This is what I'm getting.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \checkmark\]

owlet
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah i have to use ln not log :3 thanks!

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Uhh... not entirely.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[\color{red}{\log_e (x) \equiv \ln(x)}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Either 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

owlet
 one year ago
Best ResponseYou've already chosen the best response.0yeah, so if I write it in terms of log, it will be like: dw:1443325371555:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3For practice, you should try this problem: \(\large f(x) =\dfrac{e^{2x}1}{2e^2x}\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[\large f(x) = \frac{e^{2x}1}{2e^{2x}}\]

owlet
 one year ago
Best ResponseYou've already chosen the best response.0ok, I will also find the inverse of that function?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Yeah. It'll help you practice how to find inverse of logarithmic functions

owlet
 one year ago
Best ResponseYou've already chosen the best response.0ok..dw:1443325598398:dwdw:1443325667079:dw Can I simplify it more?

owlet
 one year ago
Best ResponseYou've already chosen the best response.0wait i think i did something wrong..

owlet
 one year ago
Best ResponseYou've already chosen the best response.0no i think i'm right :P dw:1443326011460:dw
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