Let \( [t] \) denote the greatest integer \( \leq t \) and \( \{t\} \) denote the fractional par...

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Let \( [t] \) denote the greatest integer \( \leq t \) and \( \{t\} \) denote the fractional part \( t \). Then integral value of \( \alpha \) for which the left hand limit of the function \( f(x)=f[1+x]+\frac{\alpha^{2[x]+\{x\}}+[x]-1}{2[x]+\{x\}} \) at \( x=0 \) is equal to \( a-\frac{4}{3} \), is
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