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The domain of the function f(x)=1/(sqrt(...

The domain of the function `f(x)=1/(sqrt(|x|-x))` is:
(A) `(-oo,oo)`
(B) `(0,oo`
(C) `(-oo,""0)`
(D) `(-oo,oo)"-"{0}`

A

`(-oo,oo) ~{0}`

B

`(-oo,oo)`

C

`(0,oo)`

D

(-oo,0)`

Text Solution

AI Generated Solution

To find the domain of the function \( f(x) = \frac{1}{\sqrt{|x| - x}} \), we need to determine the values of \( x \) for which the expression is defined. ### Step 1: Analyze the expression under the square root The expression under the square root is \( |x| - x \). For the square root to be defined and real, the expression must be greater than zero: \[ |x| - x > 0 \] ...
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