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The domain of definition of f(x) = sqrt...

The domain of definition of `f(x) = sqrt(sec^(-1){(1-|x|)/(2)})` is

A

`(-oo, -3)`

B

`[3, oo)`

C

`phi`

D

`(-oo, -3] uu [3, oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
For (x) to real, must have
`sec^(-1){(1-|x|)/(2)} gt 0 and (1-|x|)/(2) le -1 or,(1-|x|)/(2) ge1`
`rArr 1-|x| le -2 or, 1- ge2[because 0 le sec^(-1){(1-|x|/(2)} ge pi]`
`|3| ge 3 " "[because |x| le- 1 "absurd"]`
`rArr x in (-oo, -3]uu [3,oo)`
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