Find the value of `x`
for which following expressions are defined:
`1/(sqrt(x-|x|))`
(ii) `1/(sqrt(x+|x|))`
Text Solution
Verified by Experts
(i) `x-|X| ={:{(x-x=0, if x ge 0 ),(x+x = 2x,if x lt 0 ):}` `rArr x- |x| le 0, for all x ` Thus `(1)/(sqrt(x-|X|)` does not take real values for any `x in R " and " (1)/(sqrt(x-|x|)` is not defined for any `x in R` (ii) `x+|x| ={:{( x+x= 2 x if x ge 0 ),(x-x =0 ","if x le 0 ):}` Thus `(1)/(sqrt(x|x|)` is defined only when `x gt 0 `
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