inverse function question

Hey, I'm having trouble fully understanding absolute value graphs and I've been asked find the largest value of a so that f^-1 exists for the function:
f: (-efinity,a) --> R where f(x)= logel2x-1l

*note: i have used 'l' to represent the straight line indicating the it is an absolute value...

I know the answer is a=1/2 but i have no clue how to get that answer... Any help would be much appreciated :)

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  1. There is no such thing as the log of a negative number or zero. Because of the absolute value in the definition of f(x), the only value of x for which f(x) is not defined is x = 1/2.

    An inverse function of f(x) can be defined for all x, but there will be two values of f^-1(x) for each x , since two different x values, symmetric about a=1/2, give the same f(x)

    I don't know what you mean by
    f: (-efinity,a) --> R

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