$f(1)=b+1$ 

$\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,(a\left[ -x \right]+\left[ -3x \right])=a\left[ -{{(1)}^{-}} \right]+\left[ -{{(3)}^{-}} \right]=-a-3$ 

$\underset{x\to {{1}^{+}}}{\mathop{\lim }}\,\frac{x-\sqrt{x}}{1-{{x}^{2}}}=\underset{x\to 1}{\mathop{\lim }}\,\frac{1-\frac{1}{2\sqrt{x}}}{-2x}=\frac{\frac{1}{2}}{-2}=-\frac{1}{4}$ 

$\left\{ \begin{matrix}    b+1=-\frac{1}{4}\Rightarrow b=-\frac{5}{4}  \\    -a-3=-\frac{1}{4}\Rightarrow a=-\frac{11}{4}  \\ \end{matrix} \right.$ 

$\underset{x\to {{(-1)}^{-}}}{\mathop{\lim }}\,f(x)=\underset{x\to {{(-1)}^{-}}}{\mathop{\lim }}\,(-\frac{11}{4})\left[ -x \right]+\left[ -3x \right])=-\frac{11}{4}\left[ -{{(-1)}^{-}} \right]+\left[ -3{{(-1)}^{-}} \right]=\frac{-11}{4}\times 1+3=\frac{1}{4}$