The-domain-of-f-x-cos-sinx-1-x-1-sin-1-x-2-1-2x-is-

Question Number 44369 by Necxx last updated on 27/Sep/18

T h e d o m a i n o f

Missing \left or extra \right

i s \dots \dots \dots = .

Commented by Necxx last updated on 28/Sep/18

p l e a s e h e l p

Answered by tanmay.chaudhury50@gmail.com last updated on 28/Sep/18

{s i n}^{- 1} (\frac{x^{2} + 1}{2 x}) i s d e f i n e d w h e n ∣ \frac{x^{2} + 1}{2 x} ∣⩽ 1

★ x^{2} + 1 ⩽ 2 ∣ x ∣

∣ x ∣^{2} - 2 ∣ x ∣ + 1 ⩽ 0

{(∣ x ∣ - 1)}^{2} ⩽ 0 b u t {(∣ x ∣ - 1)}^{2} c a n n o t b e l e s s t h a n

z e r o s o (∣ x ∣ - 1) = 0

∣ x ∣= 1 x = \pm 1

s o d o m a i n o f {s i n}^{- 1} \frac{x^{2} + 1}{2 x} x ϵ {\pm 1}

★ ★ d o m a i n f o r \frac{1}{x - 1} x ϵ R - {1}

★ ★ ★ d o m a i n f o r \sqrt{c o s (s i n x)}

f r o m a t t a c h e x g r a p h o f \sqrt{c o s (s i n x)}

t h e d o m a i n x ϵ (- \infty, \infty)

s o r e q u i r e d a n s i s x ϵ [- 1, 1)

t h e v a l u e o f x f r o m - 1 t o + 1 e x c l u d i n g 1

p l s c h e c k \dots

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Sep/18