How to find the Inverse of f(x) = 3+x+(e^x)

[r_swayze]

?

Is it even possible?

 

[NoMoreExams]

Not explicitly, is that the full problem?

 

[r_swayze]

Well the full problem is:

If f(x) = 3+x+(e^x) , find f^-1(4)

so wouldn't I need to find the inverse first and then plug in 4?

 

[NoMoreExams]

No think about what f^(-1)(4) is, it's basically what value of x will give you 4 i.e. solve 3 + x + e^x = 4... there's an obvious value for x.

 

[r_swayze]

I know the answer is 0 if you just use trial and error or graph it out, but what if the problem was more complex? What I am having trouble with is how do solve for x when you have:

y = x + e^x

What would be the next step? I can't think of any way to extract the x

 

[NoMoreExams]

There isn't. That's the whole point of these problems, for you think what f^(-1)(blah) means. In this case it means that blah must be in the range, so they are trying to get you to figure out what it would map to in the domain without knowing explicitly what the formula would be. You COULD have approximated the value using any number of techniques if it wasn't something "nice"

 

[Dick]

You can't in any reasonably simple way. There aren't any standard functions in the book to write the answer with. If you want to find say f^(-1)(3) you just have to use numerical methods to get an approximation.

 

[bigevil]

swayze, perhaps it'd be useful to think more simply, ie, what is the relationship of the points between two inverse functions? The question only asks about one particular point, so it's pointless to find out what the entire inverse function is. (Assuming that, since the question asks about an inverse, the inverse exists.)