Find the domain of $f(x) = \sqrt{(0.625)^{4-3x} - (1.6)^{x(x+8)}}$

[-4, -1] [4, -1] [2, 5] [-5, -2]

[-4, -1]

Clearly, $(0.625)^{4-3x}≥ (1.6)^{x(x+8)}$ or $(\frac{5}{8})^{4-3x}≥(\frac{8}{5})^{x(x+8)}$ or $(\frac{8}{5})^{3x-4}≥(\frac{8}{5})^{x(x+8)}$ or $3x-4≥x^2+8x$ or $x^2+5x+4≤0$ or $-4≤x≤-1$ Hence, the domain of function f(x) is $x ∈ [-4, -1]$.