What is the domain of f(x)=(5x)/(x^2-4)-sqrt(x) ?

The domain of f(x)=(5x)/(x^2-4)-sqrt(x) is 0 2

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domain of f(x)=(5x)/(x^2-4)-sqrt(x)

domain

f (x) = \frac{5 x}{x ^{2} - 4} - x

0 \leq 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

Combine real regions and undefined points for final function domain

0 \leq x < 2 or x > 2

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

\frac{X + 4}{- 4 X + 3}

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

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

f (x) = arcsin (ln (2 x))

What is the domain of f(x)=(5x)/(x^2-4)-sqrt(x) ?
The domain of f(x)=(5x)/(x^2-4)-sqrt(x) is 0<= x<2\lor x>2