Let [t] denote the greatest integer ≤ t and {t} denote the fractional part of t. The integral value of α for which the left hand limit of the…

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