Limits Continuity And Differentiability

Let [t] denote the greatest integer \(\le\) t and {t} denote the fractional part of t. The integral value of \(\alpha\) for which the left hand limit of the function

\(f(x) = [1 + x] + {{{\alpha ^{2[x] + {\{x\}}}} + [x] - 1} \over {2[x] + \{ x\} }}\) at x = 0 is equal to \(\alpha - {4 \over 3}\), is _____________.