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.

Reply 3

Core

OP

6

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

log_ee^x

can't be the inverse.

Reply 4

Core

OP

6

Original post by ForGreatJustice

From a general theory point of view, an inverse function is such that

f^{-1}(f(x))=x

so if

f(x)=e^x

then the inverse function is

log_{e}(x)

since then

f^{-1}(f(x))=log_{e}(e^x)=x

Unparseable latex formula:

f^-^1(f(x))=x

? How is this the same as

Unparseable latex formula:

f^-^1(x)=x

and is it meant to be?

Reply 5

ForGreatJustice

13

Original post by Core

How is this the same as

Unparseable latex formula:

f^-^1(x)=x

and is it meant to be?

It's not the same, and it's not meant to be.

Reply 6

Core

OP

6

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.

Unparseable latex formula:

f^-^1(f(x))=x = f^0(x)=1(x)=x

?

Reply 7

Core

OP

6

So this is from the functions chapter isn't it, So if I try to do the opposite to

e^x

I will end up at

log_ex

ok then
how about this

Unparseable latex formula:

f(x)=e^x, f^-^1(x)=log_ex, ff^-^1(x)=x

, 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.

(edited 13 years ago)

Reply 8

Core

OP

6

Apply

Unparseable latex formula:

f(x)= e^x, ff^-^1(x)=x

so the

Unparseable latex formula:

f^-^1(x)

is a function that maps

e^x

to

x

alright i get it now.

Unparseable latex formula:

ff^-^1(x)=x

because

f(x)=e^x

making

Unparseable latex formula:

f^-^1(x) = f^-^1(e^x)

in

Unparseable latex formula:

ff^-^1(x)

and

log_ee^x = x

as log

log_ex

is the function of

Unparseable latex formula:

f^-^1

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)?

(edited 13 years ago)

Reply 9

ForGreatJustice

13

Original post by Core

Unparseable latex formula:

f^-^1(x) = f^-^1(e^x)

This isn't what you mean, surely?

But the rest of the post seems fine, I think.

Reply 10

Core

OP

6

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

Unparseable latex formula:

ff^-^1(x)=x

after applying

f(x)=e^x

you then apply

Unparseable latex formula:

f^-^1(x)=log_ex

only in the case of the composite function

x

becomex

e^x

so you have instead of

Unparseable latex formula:

f^-^1(x)=log_ex

we have

Unparseable latex formula:

f^-^1(e^x)=log_ee^x

but this is only in the case of f(x)=e^x.

Reply 11

ForGreatJustice

13

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.

Reply 12

Core

OP

6

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.