Question

The domain of the function $co{s}^{-1}(lo{g}_2(x^2+5x+8))$ is

• A. $[2,3]$
• B. $[-2,2]$
• C. $[3,1]$
• D. $(-2,-2)$
• E. $[-3,-2]$

Answer 1

Answer: (E)

Function ${\cos }^{-1}\left({\log }_2\left(x^2+5x+8\right)\right)$
The function should exist when
$-1\le {\log }_2\left(x^2+5x+8\right)\le 1$
We take only, ${\log }_2\left(x^2+5x+8\right)\le 1$
$\Rightarrow x^2+5x+8\le (2{)}^1$
$\{\because -1\le {\log }_2\left(x^2+5x+8\right)$
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 $-3\le x\le -2$