First slide

Functions (XII)

Question

The domain of the function $f (x) = \log 2 \sin x$ is

Moderate

A

$R$
B

$R ~ {n π : n \in I}$
C

$R ~ {n π : n \in N}$
D

$\cup (2 n π, (2 n + 1) π)$

Solution

$f (x) = \log 2 \sin x$ is defined for all $x$ for
which $\sin$ $x > 0 .$ But $\sin x > 0$ if $x \in (0, π) \cup (2 π, 3 π) \cup \dots$
$= \cup (2 n π, (2 n + 1) π)$ .

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