I don't know what quantity symbol I represents, but I could guess that I takes on various values as a function of some attributes (with specific values of these attributes 0 and 1 appearing as the subscript).
Function f appears to have x as its independent variable, with alpha and beta specified as parameters (i.e., variable constants which change from one application of f to another).
Perhaps, alpha=0 and beta=1 specifies one of many possible values of I.
My comments are all guesses.
Does the textbook define any of these symbols? Does it explain the scenarios under which function f is useful?
Do you know the meaning of alpha and beta?