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 ensure that the expression inside the square root is positive, as the square root cannot be negative or zero (since it is in the denominator).
### Step 1: Analyze the expression inside the square root
The expression we need to analyze is \( |x| - x \).
### Step 2: Consider two cases for \( |x| \)
1. **Case 1**: When \( x \geq 0 \)
- Here, \( |x| = x \).
...
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