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The domain of f(x)=sin^(-1)[2x^2-3],w h ...

The domain of `f(x)=sin^(-1)[2x^2-3],w h e r e[dot]` denotes the greatest integer function, is `(i)(-sqrt(3/2),sqrt(3/2))` `(ii)(-sqrt(3/2),-1)uu(-sqrt(5/2),sqrt(5/2))` `(iii)(-sqrt(5/2),sqrt(5/2))` `(iv)(-sqrt(5/2),-1)uu(1,sqrt(5/2))`

A

`(-sqrt((3)/(2)),sqrt((3)/(2)))`

B

`(-sqrt((3)/(2)),-1]cup (-sqrt((5)/(2)),sqrt((5)/(2)))`

C

`(-sqrt((5)/(2)),sqrt((5)/(2)))`

D

`(-sqrt((5)/(2)),-1]cup [1,sqrt((5)/(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
We must have `-1 le [2x^(2)-3] le 1`
or `-1 le 2x^(2)-3 lt 2 " or " 1 le x^(2) lt (5)/(2)`
or `x in (-sqrt((5)/(2)),-1] cup [1,sqrt((5)/(2)))`
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