Number of integers in domain of function `f(x) =log_(|x^2|)(4-|x|)+log_2{sqrt(x)}` is

Options

A. 0
B. 1
C. 2
D. 3

Answer

C

Explanation

`f(x)=log_([x^(2)])(4-|x|)+log_(2){sqrtx}`
`"For "4-|x|gt0rArr|x|le4 rArr-4ltxlt4`
`"For "[x^(2)]gt0,[x^(2)]ne1`
`rArr" "[x^(2)]ge2`
`rArr" "2le x^(2)lt oo`
`rArr" "sqrt2le x lt oo or -oo lt x le -sqrt2`
For `{sqrtx}gt0, sqrtx ne i rArr x ne i^(2)`
`therefore" "x=2,3`