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osanseviero
 3 years ago
Inverse logarithmic function
osanseviero
 3 years ago
Inverse logarithmic function

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osanseviero
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1\(\Large a=\ln c \implies c = e^a \)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

hartnn
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1so the range of the inverse is x>0

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

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

osanseviero
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1if you have practices enough, nothing is hard :)

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