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# inverse of the exponential watch

1. Why is the inverse of and not .
2. From a general theory point of view, an inverse function is such that

so if then the inverse function is since then
3. log(e)e^x = xlog(e)e = x.1 = x
This is clearly not the inverse of e^x!

Sketch e^x and lnx - you'll see that they are a reflection in y = x, which means that they are the inverse of each other.
4. (Original post by AnonyMatt)
log(e)e^x = xlog(e)e = x.1 = x
This is clearly not the inverse of e^x!

Sketch e^x and lnx - you'll see that they are a reflection in y = x, which means that they are the inverse of each other.
thats true, im still reading the second post, although after i went away to think i realised that can't be the inverse.
5. (Original post by ForGreatJustice)
From a general theory point of view, an inverse function is such that

so if then the inverse function is since then
? How is this the same as and is it meant to be?
6. (Original post by Core)
How is this the same as and is it meant to be?
It's not the same, and it's not meant to be.
7. (Original post by ForGreatJustice)
It's not the same, and it's not meant to be.
thankyou i was trying to make it the same in my mind and it was confusing me. ?
8. So this is from the functions chapter isn't it, So if I try to do the opposite to I will end up at ok then
how about this , opps i dont think ive dealt with functions that turn x into a power of something, but il think it over in my head and try to make sense of it, il post my thoughts, please say if they are correct.
9. Apply so the is a function that maps to alright i get it now. because making in and as log is the function of as to why this function qualifies as the inverse, is it a case of as long the I use function when acting on another function gets me back to x then this function (the one being applied) is the inverse of the other function (the one being acted upon)?
10. (Original post by Core)

This isn't what you mean, surely?

But the rest of the post seems fine, I think.
11. (Original post by ForGreatJustice)
This isn't what you mean, surely?

But the rest of the post seems fine, I think.
what i meant by that was in the composite function
after applying you then apply only in the case of the composite function becomex
so you have instead of we have but this is only in the case of f(x)=e^x.
12. I read your post, but I don't actually know what you're trying to say, or if you even saying anything. The point is the composition of a fucntion and it's inverse gives you the input argument, in this case it is x.
13. (Original post by ForGreatJustice)
I read your post, but I don't actually know what you're trying to say, or if you even saying anything. The point is the composition of a fucntion and it's inverse gives you the input argument, in this case it is x.
The point of the post was to explain to you what i meant by i was saying that this was only in the second stage of the composite function , i wanted to clear up any confusion you had about my post.
14. Ok, well

Are you fine with it now, or is anything still a problem?
15. (Original post by ForGreatJustice)
Ok, well

Are you fine with it now, or is anything still a problem?
No im fine with it now thank you.

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