A) \[[2,\text{ }3]\]
B) \[[-2,\text{ }2]\]
C) \[[3,\text{ }1]\]
D) \[(-2,-2)\]
E) \[[-3,-2]\]
Correct Answer: E
Solution :
Function\[{{\cos }^{-1}}({{\log }_{2}}({{x}^{2}}+5x+8))\] The function should exist when \[-1\le lo{{g}_{2}}\text{(}{{x}^{2}}+5x+8)\le 1\] We take only, \[lo{{g}_{2}}\text{(}{{x}^{2}}+5x+8)\le 1\] \[\Rightarrow \] \[{{x}^{2}}+5x+8\le {{(2)}^{1}}\] \[\{\because -1\le {{\log }_{2}}({{x}^{2}}+5x+8)\] given imaginary values} \[\Rightarrow \] \[{{x}^{2}}+5x+6\le 0\] \[\Rightarrow \] \[(x+2)(x+3)\le 0\] \[\Rightarrow \] \[x\in [-3,-2]\] Hence, the domain of the function is \[-3\le x\le -2\]You need to login to perform this action.
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