What is the inverse function of x + sin x ?

Click For Summary
SUMMARY

The inverse function of the expression x + sin x does not exist in terms of elementary functions. The discussion highlights that conventional methods fail to yield an explicit inverse. Instead, the Lagrange inversion theorem is suggested as a potential approach for those willing to explore advanced mathematical techniques.

PREREQUISITES
  • Understanding of inverse functions
  • Familiarity with trigonometric functions, specifically sine
  • Knowledge of the Lagrange inversion theorem
  • Basic calculus concepts
NEXT STEPS
  • Research the Lagrange inversion theorem in detail
  • Explore numerical methods for approximating inverse functions
  • Study the properties of non-elementary functions
  • Investigate other mathematical techniques for finding inverses of complex functions
USEFUL FOR

Mathematicians, students studying calculus, and anyone interested in advanced function analysis will benefit from this discussion.

arpon
Messages
234
Reaction score
16
What is the inverse function of ##x+sin x## ?
 
Mathematics news on Phys.org
It appears to be an inverse that cannot be found using conventional means. If you're up for it, you could try the Langrange inversion theorem.
 
  • Like
Likes   Reactions: arpon
arpon said:
What is the inverse function of ##x+sin x## ?

There isn't one in elementary functions.
 
  • Like
Likes   Reactions: arpon

Similar threads

Undergrad Can an inverse function of a special cubic function be found?
  • · Replies 15 ·
Replies
15
Views
3K
MHB How do trigonometric functions and their inverses relate to each other?
  • · Replies 16 ·
Replies
16
Views
2K
High School Inverse Functions vs Inverse Relations
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad No Inverse for sin(x)+x Function
  • · Replies 10 ·
Replies
10
Views
13K
Undergrad How do I do this calculation involving the SIN function?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Domain of the identity function after inverse composition
  • · Replies 3 ·
Replies
3
Views
2K
High School Are Inverse Problems More Complex Than Direct Problems in Mathematics?
  • · Replies 13 ·
Replies
13
Views
3K
MHB Finding the Inverse of f(x) = x/(x+4)
  • · Replies 2 ·
Replies
2
Views
1K
MHB What are the domain and range for the inverse function $f^{-1}$ of $f$?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Trig Functions: When Plugging in x Returns x
  • · Replies 3 ·
Replies
3
Views
2K