The domain of real valued function f(x)=$\sqrt{5-4x-x^2}$+$x^2+\log (x+4)$ is 

Given f(x)=$\sqrt{5-4x-x^2}$ +$x^2+\log (x+4)$

$$\begin{gathered} \Rightarrow 5-4x-x^2\ge 0 and x+4>0 \\ \Rightarrow x^2+4x-5\le 0 and x>-4 \\ \Rightarrow (x+5)(x-1)\le 0 and x>-4 \\ \Rightarrow x\in \left[-5,1\right] and x>-4 \\ x\in (-4,1] \end{gathered}$$

or -4$<$x$\le$1