What is the inverse of f(x) = x^3 + 2x?

[tomcenjerrym]

What is the inverse of this function $$f(x) = x^3 + 2x$$?

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$$f(x) = x^3 + 2x$$

$$y = x^3 + 2x$$

interchange $$x \Leftrightarrow y$$

$$x = y^3 + 2y$$

and it's a dead end to me ...

 

[Integral]

That will not get you where you need to be. Rather then simply interchanging x and y, you need to chang your expression for f(x) as F(y). A simple example:

f(x)= 3x + 5

y = 3x + 5

y - 5 = 3x

y/3 - 5/3 = x

x = y/3 - 5/3

so now you have x = F(y)

 

[HallsofIvy]

What you need to do is solve the equation x³+ 2x= y for x. Thats solving a fairly general cubic equation. Do you have any reason to think that the inverse can be written in a simple form?