The domain of the function f(x) = sin⁻¹((|x|+5)/(x²+1)) is (-∞, -a] U [a, ∞)
The domain of the function f(x) = sin⁻¹((|x|+5)/(x²+1)) is (-∞, -a] U [a, ∞)
Option 1 -
(√17-1)/2
Option 2 -
√17/2
Option 3 -
(√17+1)/2
Option 4 -
(1+√17)/2
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:f (x)=sin (|x|+5)/ (x²+1)
For domain:
-1 ≤ (|x|+5)/ (x²+1) ≤ 1
Since |x|+5 and x²+1 is always positive
So (|x|+5)/ (x²+1) ≥ 0 ∀x∈R
So for domain:
(|x|+5)/ (x²+1) ≤ 1
⇒ |x|+5 ≤ x²+1
⇒ 0 ≤ x²-|x|-4
⇒ 0 ≤ (|x|- (1+√17)/2) (|x|- (1-√17)/2)
⇒ |x| ≥ (1+√17)/2 or |x|≤ (1-√17)/2 (Rejected)
⇒ x∈ (-∞, - (1+√17)/2] ∪ [ (1+√17)/2, ∞)
So, a = (1+√17)/2
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