First slide

Functions (XII)

Question

The domain of $f (x) = \sin^{- 1} [2 x^{2} - 3],$ where [.] denotes the greatest integer function, is

Moderate

A

$(- \sqrt{\frac{3}{2},} \sqrt{\frac{3}{2}})$
B

$(- \sqrt{\frac{3}{2}}, - 1] \cup (- \sqrt{\frac{5}{2}}, \sqrt{\frac{5}{2}})$
C

$(- \sqrt{\frac{5}{2}}, \sqrt{\frac{5}{2}})$
D

$(- \sqrt{\frac{5}{2}}, - 1] \cup [1, \sqrt{\frac{5}{2}})$

Solution

We must have $- 1 \leq [2 x^{2} - 3] \leq 1$
or $- 1 \leq 2 x^{2} - 3 < 2 or 1 \leq x^{2} < \frac{5}{2}$
or $x \in (- \sqrt{\frac{5}{2}}, - 1] \cup [1, \sqrt{\frac{5}{2}})$

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