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Find the value of x for which of followi...

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