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

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

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

domain

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

\frac{1}{2} \leq x < 2 or x > 2

Interval Notation

[\frac{1}{2}, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{1}{2}

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

\frac{1}{2} \leq x < 2 or x > 2

x^{3} - 11

x^{3} - 12

f (x) = x (x - 8)

\frac{x - 4}{2 x - 6}

f (x) = ln (\frac{1}{3} x - 4)

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