What is the domain of f(x)= 1/(sqrt(1-|2x|)) ?

The domain of f(x)= 1/(sqrt(1-|2x|)) is -1/2 <x< 1/2

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domain of f(x)= 1/(sqrt(1-|2x|))

domain

f (x) = \frac{1}{1 - ∣ 2 x ∣}

- \frac{1}{2} < x < \frac{1}{2}

Interval Notation

(- \frac{1}{2}, \frac{1}{2})

Solution steps

Find non-negative values for radicals:

- \frac{1}{2} \leq x \leq \frac{1}{2}

Find undefined (singularity) points:

x = - \frac{1}{2}, x = \frac{1}{2}

Combine real regions and undefined points for final function domain

- \frac{1}{2} < x < \frac{1}{2}

What is the domain of f(x)= 1/(sqrt(1-|2x|)) ?
The domain of f(x)= 1/(sqrt(1-|2x|)) is -1/2 <x< 1/2