Thread: What's the inverse of g(x) = 3 + x + e^x

1. What's the inverse of g(x) = 3 + x + e^x

g(x) = 3 + x + e^x

2. Originally Posted by TGS
g(x) = 3 + x + e^x

is this the original question, or did it arise from working out something else?

3. its the original question, but i just solved it so nevermind.

Thanks though.

4. Originally Posted by TGS
its the original question, but i just solved it so nevermind.

Thanks though.
is that so ? I would love to see how you found $g^{-1}(x)$.

5. Originally Posted by skeeter
is that so ? I would love to see how you found $g^{-1}(x)$.
me too

6. $y=3+x+e^{x}$

$e^{y-3}=e^{x+e^x}$

Now putting it in standard Lambert-W terms:

$e^{y-3}=e^x e^{e^x}$

so:

$e^x=W(e^{y-3})$

but:

$y-3-x=e^{x}$

then:

$x=y-3-W(e^{y-3})$

. . . end special function discrimination. Equal rights for special functions.

7. I was hoping for a non-Lambert W function algebraic miracle.

8. Can someone please provide a simple method to determine this answer? I don't recall how to deal with two variables in an inverse situation especially with one as an exponent. Thanks!

9. Originally Posted by Atinus
Can someone please provide a simple method to determine this answer? I don't recall how to deal with two variables in an inverse situation especially with one as an exponent. Thanks!
If you read this thread while awake you would realise that a 'simple method' is not possible (unless you consider using the Lambert W-function simple).