Question

What's the `f^(-1)(x)` of `f(x)=x^3+1/x+2 ?`

Answer 1

It is not going to be easy.... It involves `x` to the `3`rd and `4`th powers, which are extremely ugly to solve.

Explanation:

We say that `f^-1(x)` is the inverse function of `f(x)`. That means, if `f(x)=y=...x+...`, we express `x` in terms of `y`.

`f(x)=x^3+1/x+2`

`y=x^3+1/x+2`

`x^4+2x+1=xy`

From here, I couldn't solve it, so I used Wolfram-Alpha, and got the following result:

http://www4d.wolframalpha.com/Calculate/MSP/MSP17521a097e687h3i88f00003705i975e921gb8a?MSPStoreType=image/gif&s=39&w=541.&h=544.