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

Options

A. `(0,1)`
B. `(0,1]`
C. `[1,oo)`
D. `(1,oo)`

Answer

A

Explanation

`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`