invert a function: f(x) = 4 + x + 5*exp(x - 3)

[kjd]

I posted this under algebra/pre-calc, but the reply suggests that more sophisticated techniques are needed, so I'm trying again.

Is there a closed form for the inverse of this function and if so, what is it?

f(x) = 4 + x + 5*exp(x - 3)

 

[pka]

DO NOT DOUBLE POST!
The answer you were given is perfectly adequate.
The fact is: there is an inverse function because the derivative is always positive.
However, there is no elementary closed form for that function.

 

[galactus]

I ran it through Maple and this is what she gave me:

\(\displaystyle \L\\x=y-4-LambertW(\frac{5e^{y}}{e^{7}})\)

I don't really know what LambertW means.

May have something to do with infinite solutions for ye^y. I don't know. Interesting quest to find out.

 

[skeeter]

Lambert W function

 

[galactus]

Thanks, skeeter. I also found a more comprehensive explanation at Wikipedia.

http://en.wikipedia.org/wiki/Lambertw

 

[tkhunny]

I wonder why I picked something with a "W" in it for my original response...

It is an interesting thing, W.