Mathematics - Limits Question with Solution | TestHub

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