A) \[[-3,2]\]
B) \[[1,4]\]
C) \[[2,5]\]
D) \[[-4,-1]\]
Correct Answer: D
Solution :
[d] Clearly, \[{{(0.625)}^{4-3x}}\ge {{(1.6)}^{x(x+8)}}\] or \[{{\left( \frac{5}{8} \right)}^{4-3x}}\ge {{\left( \frac{8}{5} \right)}^{x(x+8)}}\] or \[{{\left( \frac{8}{5} \right)}^{3x-4}}\ge {{\left( \frac{8}{5} \right)}^{x(x+8)}}\] or \[3x-4\ge {{x}^{2}}+8x\] or \[{{x}^{2}}+5x+4\le 0\] or \[-4\le x\le -1\] Hence, the domain of function \[f(x)\] is \[x\in [-4,-1]\]
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