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

The domain of f(x)=(x-2)/(x^2-4)+1/(sqrt(x)) is 0 2

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

domain

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

0 < x < 2 or x > 2

Interval Notation

(0, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = 2, x = - 2, x = 0

Combine real regions and undefined points for final function domain

0 < x < 2 or x > 2

\frac{2}{3}

f (x) = x^{3} + 4 x^{2}

\frac{x ^{2} + 8}{x ^{2} - 4}

f (x) = \frac{8}{x ^{2} - x - 6}

ln (ln (x))

What is the domain of f(x)=(x-2)/(x^2-4)+1/(sqrt(x)) ?
The domain of f(x)=(x-2)/(x^2-4)+1/(sqrt(x)) is 0<x<2\lor x>2