The domain of the function is

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The domain of the function f(x)=sin⁡−11∣x2−1∣+1sin⁡2x+sin⁡x+1f(x) = \sin^{-1} \frac{1}{|x^2 - 1|} + \frac{1}{\sqrt{\sin^2 x + \sin x + 1}} is (1) (−∞,∞)(-\infty, \infty) (2) (−∞,−2]∪[2,∞)(-\infty, -\sqrt{2}] \cup [\sqrt{2}, \infty) (3) (−∞,−2]∪[2,∞)∪{0}(-\infty, -\sqrt{2}] \cup [\sqrt{2}, \infty) \cup \{0\} (4) None of the above

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