What is the domain of f(x)=(2x-1)/(sqrt(1-4x^2)) ?

The domain of f(x)=(2x-1)/(sqrt(1-4x^2)) is -1/2 <x< 1/2

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domain of f(x)=(2x-1)/(sqrt(1-4x^2))

domain

f (x) = \frac{2 x - 1}{1 - 4 x ^{2}}

- \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}

f (x) = 5 x + 3

\frac{x ^{2} - 5 x + 1}{x ^{2} - 1}

2 x^{2} - 7 x - 4

\frac{- 5 x + 8}{6 x - 10}

f (x) = \frac{x + 2}{x - 2}

What is the domain of f(x)=(2x-1)/(sqrt(1-4x^2)) ?
The domain of f(x)=(2x-1)/(sqrt(1-4x^2)) is -1/2 <x< 1/2