how to find function,inverse function and y=x of
f(x)=e^x

Question

how to find function,inverse function and y=x of
f(x)=e^x

anonymous · Answer

Is your question just how do you find the inverse function of f(x) = e^x?

deadpool · Answer

either one would be a big help

anonymous · Answer

okay, to find the inverse of a function, we first write the equation as y = e^x

with this equation, you want to get x by itself, so you take the natural log of both sides

ln y = ln(e^x)    

Are you following so far? What do you get for x?

deadpool · Answer

ln y = x ln e
but isnt e the natural log already?

anonymous · Answer

no e is a mathematical constant, like pi. the natural log is a logarithm with base e, like $$\log_{e} $$
when you take the natural log of e, everything cancels and you are left with its power.. like

$$\ln (e ^{x}) = x$$

so x = lny
Let me find something on natural log, meanwhile lmk when you're caught up

anonymous · Answer

ah http://en.wikipedia.org/wiki/Natural_logarithm should be good enough, just a quick look

deadpool · Answer

ok so the answer would be ln y = x ln e?

anonymous · Answer

while that is legal, you want to get x alone so it is better to simplify
lny = ln(e^x)    to lny = x

then you switch the variables to get lnx = y
this is the inverse function

$$f ^{-1}(x) = lnx$$

Just to make things more clear the steps to get the inverse of a function are
1. Get x by itself
2. Switch Variables

anonymous · Answer

also, the way you did it was perfectly fine since ln(e) = 1

deadpool · Answer

thank you so much!

anonymous · Answer

np :)