Find the domain of f(x) = √((0.625)^4-3x - (1.6)^x(x+8))

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 $x ∈ [-4, -1]$.