First slide

Functions (XII)

Question

The domain of $f (x) = \sqrt{\sin x} + \sqrt{16 - x^{2}}$ is

Moderate

A

$[- 4 . - π] \cup [0, π]$
B

$[- 4, - π]$
C

$[0, π]$
D

Nnone of these

Solution

$\begin{array}{l} f (x) = \sqrt{\sin x} + \sqrt{16 - x^{2}} \\ or \sin x \geq 0 and 16 - x^{2} \geq 0 \\ or 2 n π \leq x \leq (2 n + 1) π, n \in Z and - 4 \leq x \leq 4 \\ Therefore, domain is [- 4, - π] \cup [0, π] . \end{array}$

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