Find the domain of the function : `f(x)=sqrt(((log)_(0. 2)|x-2|)/(|x|))`

Answer

`[1,2) cup (2,3]`

Explanation

`f(x)=sqrt((log_(0.3)|x-2|)/(|x|))." Here " |x| gt 0 AA x in R-{0} " (1)" `
Therefore, for `f(x)` to get defined,
`log_(0.3)|x-2| ge 0`
or ` 0 lt |x-2| le 1`
or ` |x-2| le 1 " and " x ne 2`
or ` -1 le x-2 le 1 " and " x ne 2`
or `1 le x le 3 " and " x ne 2`
or `x in [1,2) cup (2,3]`