Inverse function of hypergeometric function, e.g., ${}_{2}F_{1}(1,1;1.2;x)$

Question

I want to know whether it is able to express the inverse function of hypergeometric function using some special function.

For instance, the Gauss hypergeometric function $f(x)={}_{2}F_{1}(1,1;1.2;x)$. I want to solve the equation $f(x)=-0.2$. One way to get $x$ is to use Matlab and plots. But I am wondering if it is possible to express the inverse function of hypergeometric functions using some special functions (E.g., the Lambert W function can be used to express the inverse function of $z\cdot e^{z}$).

Thanks in advance.