The domain of the function f(x)=sin−1⁡(3−x)ln⁡(|x|−2) is

fx =sin-13-xlogx-2 let gx = sin-13-x then -1≤3-x≤1 ⇒1≥x-3≥-1 ⇒4≥x≥2 ⇒ domain of gx= D1=2,4 let hx =logx-2 then x-2 >0 ⇒x>2 ⇒ domain of hx=D2=-∞,-2∪2,∞ ⇒domain of fx= D1∩D2-x∈R/ hx=0 = (2, 4] -3 since hx=0 ⇒ x-2=1⇒x=±3

The domain of the function f(x)=sin−1⁡(3−x)ln⁡(|x|−2) is

fx =sin-13-xlogx-2 let gx = sin-13-x then -1≤3-x≤1 ⇒1≥x-3≥-1 ⇒4≥x≥2 ⇒ domain of gx= D1=2,4 let hx =logx-2 then x-2 >0 ⇒x>2 ⇒ domain of hx=D2=-∞,-2∪2,∞ ⇒domain of fx= D1∩D2-x∈R/ hx=0 = (2, 4] -3 since hx=0 ⇒ x-2=1⇒x=±3

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

$The domain of the function f (x) = \frac{\sin^{- 1} (3 - x)}{\ln (| x | - 2)} is$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$[2, 4]$

$(2, 3) \cup (3, 4]$

$[2, \infty)$

$(- \infty, - 3) \cup [2, \infty)$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$f (x) = \frac{\sin^{- 1} (3 - x)}{\log (|x| - 2)} l e t g (x) = \sin^{- 1} (3 - x) t h e n - 1 \leq 3 - x \leq 1 \Rightarrow 1 \geq x - 3 \geq - 1 \Rightarrow 4 \geq x \geq 2 \Rightarrow d o m a i n o f g (x) = D_{1} = [2, 4]$

$l e t h (x) = \log (|x| - 2) t h e n |x| - 2 > 0 \Rightarrow |x| > 2 \Rightarrow d o m a i n o f h (x) = D_{2} = (- \infty, - 2) \cup (2, \infty) \Rightarrow d o m a i n o f f (x) = D_{1} \cap D_{2} - \{x \in R / h (x) = 0\}$