Help finding a inverse function

[farmd684]

Homework Statement

Given that f(x)=2x^3+5x+3 and f^-1(x)=1 then find the value of x
Given that f(x)=x^3/(x^2+1) and f^-1(x)=2 then find the value of x

Homework Equations

I got to the eqn x=2Y^3+5Y+3 & X=Y^3/(Y^2+1)

The Attempt at a Solution

But now i m in trouble finding the f^-1(x) in explicit form to use the value of f^-1(x)

 

[Dick]

You are going to have a hard time finding explicit forms. But you don't have to. If e.g. f^(-1)(x)=1, then x=f(1), yes?

 

[farmd684]

Thanks that got my problem solved :D
But i m just curious to know how to find that big cubic or quadratic functions in explicit mode :)

 

[Dick]

If it cubic or quartic, there are formulas, but they are too complicated for most practical uses. If it's fifth degree or worse there are no formulas, except in special cases. There are proofs of this, it's called Galois theory.