What is the Inverse of the Function f(x) = e^x + e^(-x) + 1?

  • Context: Undergrad 
  • Thread starter Thread starter Eishan M
  • Start date Start date
  • Tags Tags
    Function Inverse
Click For Summary

Discussion Overview

The discussion centers around finding the inverse of the function f(x) = e^x + e^(-x) + 1. Participants explore various methods and approaches to derive the inverse, focusing on mathematical reasoning and transformations.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses intimidation by the problem and seeks assistance in reaching a conclusion.
  • Another participant suggests starting with the equation e^x + e^(-x) + 1 = y as a way to approach the problem.
  • A further suggestion involves converting the problem into a quadratic equation by letting u = e^x, leading to the equation u^2 + 1 + u(1 - y) = 0, and then solving for u as a function of y before finding x = ln(u).

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on a definitive method or solution for finding the inverse, indicating that multiple approaches are being considered without resolution.

Eishan M
Messages
2
Reaction score
0
Hi,
What is the inverse of f(x)= e^x + e^-x +1?
 
Physics news on Phys.org
This question has been intimidating me for quite a while. I'm unable to reach a definite conclusion to this. Please help
 
Try solving $$e^x+e^{-x}+1=y.$$
 
Convert problem into a quadratic equation by u=e^x,\ u^2+1+u(1-y)=0. Get u as a function of y, then x=ln(u).
 

Similar threads

Undergrad Local inverse of non bijective functions
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Existence and Uniqueness of Inverses
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Is -1 in U=eiA an Exponent or an Inverse?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Is the solution to this problem as trivial as I think?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Dfns group action & group, written in terms of the other
  • · Replies 26 ·
Replies
26
Views
1K
Undergrad How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
  • · Replies 48 ·
2
Replies
48
Views
5K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad What are the Eigenvalues of the Hermitian Inverse \(H^{-1}\)?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Meaning of ##\coprod_{x\in\mathrm{Spec}R}R/\mathfrak{p}_x##
  • · Replies 11 ·
Replies
11
Views
2K
MHB Approximation of eigenvalue with inverse iteration method
  • · Replies 2 ·
Replies
2
Views
1K