Finding the Inverse of a Function with a Trigonometric Term

  • Thread starter Thread starter Joe_K
  • Start date Start date
  • Tags Tags
    Inverse
Click For Summary

Homework Help Overview

The discussion revolves around finding the inverse of the function f(x) = x + cos(x). Participants are exploring the challenges associated with isolating x within the cosine function and the implications for determining the inverse.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the difficulty of solving the equation for x due to the presence of the cosine function. There are inquiries about whether substituting specific values, such as f^-1(1), is a valid approach to understanding the inverse function. Some participants question the existence of a general expression for the inverse.

Discussion Status

There is an ongoing exploration of how to approach the problem, with some participants suggesting that a general solution may not be feasible. Guidance has been offered regarding the possibility of evaluating specific values without needing a full expression for the inverse.

Contextual Notes

Participants note that the problem may be simplified by focusing on specific values rather than attempting to find a general inverse. There is also a recognition of the limitations imposed by the nature of the function involved.

Joe_K
Messages
32
Reaction score
0

Homework Statement



f(x)= x+cosx

find the inverse, f^-1(x)



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.
 
Physics news on Phys.org
Your memory of how to do it is fine, but you can't solve this one for x algebraically.
 
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?
 
Joe_K said:
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?

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?
 
Yes, thank you for your help!
 
Joe_K said:

Homework Statement



f(x)= x+cosx

find the inverse, f^-1(x)



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.

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?
 

Similar threads

  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 12 ·
Replies
12
Views
4K
Replies
13
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K