Numerical Analysis — inverse of Lagrange interpolation polynomial

Suppose $g$ is function such that $y = f(x) \Leftrightarrow x = g(y)$ and $f(x)$ is given by $f(x) = \frac{(x-b)(x-c)}{(a-b)(a-c)}\alpha + \frac{(x-a)(x-c)}{(b-a)(b-c)}\beta + \frac{(x-a)(x-b)}{(c-a)(c-b)}\gamma$ where $a < b < c$ and $\alpha < \beta < \gamma$ are real numbers. What is $g(\beta)$ equal to?