find-the-domain-f-x-1-sin-sin-x-

Question Number 71448 by aliesam last updated on 15/Oct/19

f i n d t h e d o m a i n

f (x) = \frac{1}{s i n (s i n (x))}

Commented by kaivan.ahmadi last updated on 15/Oct/19

s i n (s i n x) = 0 \Rightarrow s i n x = k π; k \in Z

b u t s i n c e - 1 ⩽ s i n x ⩽ 1 s o - 1 ⩽ k π ⩽ 1 \Rightarrow k = 0 \Rightarrow

s i n x = 0 \Rightarrow x = k π; k \in Z

\Rightarrow D_{f} = R - {k π ∣ k \in Z}