# Help with finding inverse

1. Sep 11, 2011

### Joe_K

1. The problem statement, all variables and given/known data

f(x)= x+cosx

find the inverse, f^-1(x)

3. The attempt at a solution

To start, I tried to solve the original equation for x. But this is where I am having trouble. How do you get x by itself when it is trapped within the cos function? I used to know how to do this but I seem to have forgotten. Once I solve the equation for x, I should be able to switch the "x" and "y" terms and be left with the inverse of the original function. Maybe someone can help me remember how to get the 'x' by itself. Thank you.

2. Sep 11, 2011

### LCKurtz

Your memory of how to do it is fine, but you can't solve this one for x algebraically.

3. Sep 11, 2011

### Joe_K

What do I need to do, in order to do the problem correctly? The question in my book is asking to find f^-1(1). Should I just plug in '1' for y in the equation and solve? I believe that would only leave zero as a possible answer?

4. Sep 11, 2011

### LCKurtz

Undoubtedly the reason they asked that simpler question is because you can't do the general one. So, yes. Obviously x = 0 is a value solving 1 = x + cos(x). Do you see how to show it is the only solution or, for that matter, that the inverse function exists?

5. Sep 11, 2011

### Joe_K

Yes, thank you for your help!

6. Sep 11, 2011

### Dick

I don't think you are going to find a nice expression for f^(-1)(x). You can probably answer some questions about f^(-1) without having an expression for it. Is that the whole question?