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Question: Domain of f(x) = sin<sup>-1</sup>[2x<sup>2</sup> – 3], where [.] denotes the greatest integer functi...

Domain of f(x) = sin-1[2x2 – 3], where [.] denotes the greatest integer function, is

A

(−32,32)\left( - \frac { \sqrt { 3 } } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)

B

(−32,−1]∪[1,32)\left( - \frac { \sqrt { 3 } } { 2 } , - 1 \right] \cup \left[ 1 , \frac { \sqrt { 3 } } { 2 } \right)

C

(−52,52)\left( - \frac { \sqrt { 5 } } { 2 } , \frac { \sqrt { 5 } } { 2 } \right)

D

(−52,−1]∪[1,52)\left( - \frac { \sqrt { 5 } } { 2 } , - 1 \right] \cup \left[ 1 , \frac { \sqrt { 5 } } { 2 } \right)

Answer

(−52,−1]∪[1,52)\left( - \frac { \sqrt { 5 } } { 2 } , - 1 \right] \cup \left[ 1 , \frac { \sqrt { 5 } } { 2 } \right)

Explanation

Solution

We must have -1 ≤ [2x2 − 3] ≤ 1

⇒ 1 ≤ 2x2 – 3 < 2 ⇒ 1 ≤ x2 ≤ 52\frac { 5 } { 2 }

⇒ x ∈ (−52,−1]∪[1,52)\left( - \sqrt { \frac { 5 } { 2 } } , - 1 \right] \cup \left[ 1 , \sqrt { \frac { 5 } { 2 } } \right)