What is the inverse function of 2x+sinx?

What is the inverse function of 2x+sinx?

Summary of research on reciprocal functions



The converse of the rational function

The converse of a rational function is also a rational function. It can be found using a graph or algebraically.



Theorem of reciprocal functions

  • The reciprocal function is continuous and strictly monotonic in the same direction of monotonicity as the original function.
  • If the original function is differentiable at a point, then its inverse function is differentiable at any point image of x such that the derivative of the original function is not zero.


Existence of the inverse function

A function admits a reciprocal if every element of the starting set corresponds to a unique element of the ending set, and if every element of the ending set corresponds to a unique element of the starting set.



Establish the expression for the inverse function

Two functions f and g are reciprocal of each other if, for all a, the image of a by the function f is b, then the image of b by the function g is a.

What is the inverse function of 2x+sin(x)?

To determine the reciprocal function of 2x+sin(x), it is necessary to find a function g(x) such that g(2x+sin(x)) = x. This search can be done by solving the equation g(2x+sin(x)) = x algebraically.

The opinion of our editorial staff

To determine the inverse function of 2x+sin(x), it is recommended to use algebraic methods to solve the corresponding equation and find the inverse function. It is also important to ensure that the initial function is indeed invertible to guarantee the existence of a reciprocal function.

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