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Domain of definition of the function f(x...

Domain of definition of the function `f(x) = log_2 (-log_(1/2) (1+x^(-4))-1)` is

A

`(0,1)`

B

`(0,1]`

C

`[1,oo)`

D

`(1,oo)`

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)` is defined if
`-log_(1//2)(1+(1)/(x^(1//4)))-1 gt 0`
or ` log_(1//2)(1+(1)/(x^(1//4))) lt -1`
or `1+(1)/(x^(1//4)) gt ((1)/(2))^(-1)`
or `(1)/(x^(1//4)) gt 1`
or `0 lt x lt 1`
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