The domain of the function ^ -1 ( _2 (x^2+5 x+8 ) ) is - Vidyadip

MCQ

The domain of the function $\cos ^{-1}\left(\log _2\left(x^2+5 x+8\right)\right)$ is

A
[2,3]
B
[-2,2]
C
[3,1]
✓
[-3,-2]

✓

Answer

Correct option: D.

[-3,-2]

(D)
$-1 \leq \log _2\left(x^2+5 x+8\right)<1$
$\Rightarrow \frac{1}{2} \leq\left(x^2+5 x+8\right) \leq 2$
$\Rightarrow x^2+5 x+\frac{15}{2} \geq 0$
$\Rightarrow x^2+2\left(\frac{5}{2}\right) x+\left(\frac{5}{2}\right)^2-\left(\frac{5}{2}\right)^2+\frac{15}{2} \geq 0$
$\Rightarrow\left(x+\frac{5}{2}\right)^2+\frac{5}{4} \geq 0$ and $x^2+5 x+6 \leq 0$
$\Rightarrow(x+3)(x+2) \leq 0$
$\Rightarrow x \in[-3,-2]$

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