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.