Question
Download Solution PDFWhat is the domain of the function f(x) = sin-1 (x + 1) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Domin of sin-1 x is [-1, 1]
Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged.
Calculation:
Given: f(x) = sin-1 (x + 1)
As we know, domin of sin1 x is [-1, 1]
Therefore, -1 ≤ (x + 1) ≤ 1
subtracting 1 in above inequality,
⇒ -1 - 1 ≤ x + 1 - 1 ≤ 1 - 1
⇒ -2 ≤ x ≤ 0
∴ Domin of sin-1 (x + 1) is [-2, 0]
Mistake Points[-2, 0] is different from [-2, 0). '[' and ']' indicates that the end number (2 and 0) is also included. '(' and ')' indicates that 2 and 0 are not taken into consideration.
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