Hard Maths Problem

see for showing 1/a ln|x| is inverse of e^(ax)

i see interchanging x and y works for this problem but say you take

y=8-2x, how do u prove the inverse is (8-y)/2

here u have to rearrange it so u have x=...

like so...

y=8-2x
x=-(y-8)/2=(8-y)/2
then since f(x) =y , x=f^-1(y)
:. f^-1(y)=(8-y)/2
and so F^-1(x) = (8-x)/2

Hence my question is simply - how do u know which method to use and if both are valid how would u use method 2 to prove 1/aln|x| is the inverse of
e^(ax)

Reply 1

*bobo*

8

latentcorpse

see for showing 1/a ln|x| is inverse of e^(ax)

i see interchanging x and y works for this problem but say you take

y=8-2x, how do u prove the inverse is (8-y)/2

here u have to rearrange it so u have x=...

like so...

y=8-2x
x=-(y-8)/2=(8-y)/2
then since f(x) =y , x=f^-1(y)
:. f^-1(y)=(8-y)/2
and so F^-1(x) = (8-x)/2

Hence my question is simply - how do u know which method to use and if both are valid how would u use method 2 to prove 1/aln|x| is the inverse of
e^(ax)

use this method for equations involving logarithms and exponentials:

y=1/a ln lxl
x=1/a ln lyl
ax= ln lyl
y= e^ax

however for the question and answer you gave above it is just a matter of rearranging the formula.