I need to find an inverse function of my equation. However, the output shows a RootOf in the equation. How can I get the inverse of my equation?

syms x a b h1 h2 l

y=(h2*(x - b*x)^3)/3 - (a^3*h2*x^3)/3 + (a^4*h1*x^4)/4 - (a^3*x^3*(h1 - h2))/4 + (b*h2*x^3*(3*b^2 - 8*b + 6))/12; l=finverse(y,x)

output:

RootOf(3*a^4*h1*z^4 + 4*b^2*h2*z^3 - 3*a^3*h1*z^3 - 6*b*h2*z^3 + 4*h2*z^3 - b^3*h2*z^3 - a^3*h2*z^3 - 12*x, z)

Answer 1

[Roger Stafford]

Finding the inverse of your function amounts to solving for x as a function of y. Unfortunately this is a quartic equation in x and in general it has either four real roots, two real roots, or none. In other words, except for special values of y it will never have a single uniquely defined x root. Thus there is no unique inverse function to your equation and you had better rethink your problem.