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Question
Find the domain of the following
`f(x) = sin^-1 ((x^2 + 1)/(2x))`
Solution
The range of sin–1x is – 1 to 1
`- 1 ≤ (x^2 + 1)/(2x) ≤ 1`
⇒ `(x^2 + 1)/(2x) ≥ - 1` or `(x^2 + 1)/(2x) ≤ 1`
⇒ x2 + 1 ≥ – 2x or x2 + 1 ≤ 2x
⇒ x2 + 1 + 2x ≥ 0 or x2 + 1 – 2x ≤ 0
⇒ (x + 1)2 ≥ 0 or (x – 1)2 ≤ 0 which is not possible
⇒ – 1 ≤ x ≤ 1 or
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