How to write x as a function of f(x)?

Hi, I was wondering if there exists some code or function to change for example:

f(x) = (x^2 - 1); or any other polynomial

to

x = sqrt(f(x) + 1) This is just an example.

Basically i would want any function written as f(x) in function of x changed to x in function of f(x).

Answer 1

[Star Strider]

The Symbolic Math Toolbox has the finverse function:

syms x 
f(x) = (x^2 - 1);
finv = finverse(f)

producing:

finv(x) = 
(x + 1)^(1/2)

To do this numerically, use the fsolve function, for example:

x = fsolve(@(x)(x.^2-1) - y, x0)

where ‘y’ is the value to solve ‘x’ for, and ‘x0’ is the intial estimate.