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osanseviero
 one year ago
Inverse logarithmic function
osanseviero
 one year ago
Inverse logarithmic function

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osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1So they want the inverse of \[F(x)=\ln \sqrt{x}\] So the inverse is \[x=\ln \sqrt{y}\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large a=\ln c \implies c = e^a \)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1\[y=\left( e ^{x} \right)^{2}\] the 2 can go down, right?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large (e^x)^2 = e^{2x}\)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1oops, another silly mistake

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Can someone help me demostrate that (FoFinverse)(x)=(FinverseoF)(x)=x ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1demonstrate ? you have a function for verifying that ?

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1The one we just did

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1\[\ln \sqrt{e ^{2x}} = e ^{2\ln \sqrt{x}}=x\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1so, f inverse = e^2x just plug in x =ln \sqrt x oh, you did it :)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1But how and why? (I think that was a good statement)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1And how would that be x?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\sqrt {(e^x)^2} = e^x \\ \ln e^x = x \ln e = x\)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1so the left one is kinda obvious, so it is x

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Oh...and the other one is with \[a ^{logaN}=\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\huge a^{\log_aN}=N\)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1:) Now I understand, thanks for fifth time, just one more question :P

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Which would be the domain and the range of the first, normal function?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1since its sqrt x, x>= 0 since its ln, sqrt x >0 in all, x>0

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1so the range of the inverse is x>0

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Wish me good luck tomorrow

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yes! best of luck! hope you get full marks :)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1I hope so, this will be a hard examn...all types of functions, trigonometric identities, operations with functions

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1if you have practices enough, nothing is hard :)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Thanks for the help all night!
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